Sequence Database

A database with 1693109 machine generated integer and decimal sequences.

Displaying result 0-99 of total 30551. [0] [1] [2] [3] [4] ... [305]

Sequence pv1sq0qzw5fdm

0, 0.7615941559557649, 0.9640275800758169, 0.9950547536867305, 0.999329299739067, 0.9999092042625951, 0.9999877116507956, 0.9999983369439447, 0.9999997749296758, 0.999999969540041, 0.9999999958776927, 0.9999999994421064, 0.9999999999244973, 0.9999999999897818, 0.9999999999986171, 0.9999999999998128, 0.9999999999999747, 1, 1, 1, 1, 1, 1, 1, 1, more...

decimal, monotonic, +

a(n)=tanh(n)
n≥0
2 operations
Trigonometric
a(n)=sin(atan(sinh(n)))
n≥0
4 operations
Trigonometric

Sequence brsi1x4psomni

0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 5, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 5, 2, 3, more...

integer, non-monotonic, +, A001222

a(n)=Ω(n)
Ω(n)=max distinct factors of n
n≥1
2 operations
Prime
a(n)=log(sqrt(exp(Ω(n²))))
Ω(n)=max distinct factors of n
n≥1
6 operations
Prime
a(n)=Ω(n*p(n))-1
p(n)=nth prime
Ω(n)=max distinct factors of n
n≥1
7 operations
Prime

Sequence g3fycrmfjmnxl

0, 1, 1, 3, 4, 2, 10, 4, 1, 1, 1, 1, 2, 7, 306, 1, 5, 1, 2, 1, 5, 1, 1, 1, 1, 7, 1, 4, 2, 15, 1, 2, 1, 1, 4, 1, 3, 3, 5, 4, 1, 1, 1, 4, 3, 1, 38, 1, 2, 4, more...

integer, non-monotonic, +, A019474

a(n)=contfrac[W1]
W1=0.5671... (Lambert W)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant
a(n)=contfrac[log(W1)]
W1=0.5671... (Lambert W)
contfrac(a)=continued fraction of a
n≥0
3 operations
Power

Sequence 5ey1pvojvkhlg

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, more...

integer, strictly-monotonic, +, A000217

a(n)=∑[n]
∑(a)=partial sums of a
n≥0
2 operations
Variable
a(n)=n+a(n-1)
a(0)=0
n≥0
3 operations
Recursive
a(n)=-∑[-n]
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=∑[C(n, a(n-1))]
a(0)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=∑[and(n, -1)]
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
5 operations
Bitwise

Sequence hr1xwu5kzwtrb

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, more...

integer, strictly-monotonic, +, A000290

a(n)=n²
n≥0
2 operations
Power
a(n)=Δ[n²]+a(n-1)
a(0)=0
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=C(n, sqrt(a(n-1)))²
a(0)=0
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=∑[2*n]-n
∑(a)=partial sums of a
n≥0
6 operations
Arithmetic
a(n)=∑[or(1, 1+a(n-1))]
a(0)=0
or(a,b)=bitwise or
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence sxgqtfmeezvbp

1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, more...

integer, non-monotonic, +-, A008836

a(n)=λ(n)
λ(n)=Liouville's function
n≥1
2 operations
Prime
a(n)=(-1)^Ω(n)
Ω(n)=max distinct factors of n
n≥1
5 operations
Prime
a(n)=μ(or(6, Ω(n)))
Ω(n)=max distinct factors of n
or(a,b)=bitwise or
μ(n)=Möbius function
n≥1
5 operations
Prime

Sequence fgxbahcl0w5q

1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, more...

integer, monotonic, +, A000142

a(n)=n!
n≥0
2 operations
Combinatoric
a(n)=n*a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=∏[C(n, a(n-1))]
a(0)=1
C(n,k)=binomial coefficient
∏(a)=partial products of a
n≥0
4 operations
Combinatoric
a(n)=lcm(n!, a(n-1))
a(0)=1
lcm(a,b)=least common multiple
n≥0
4 operations
Combinatoric
a(n)=n*lcm(a(n-1), a(n-2))
a(0)=1
a(1)=1
lcm(a,b)=least common multiple
n≥0
5 operations
Recursive

Sequence k0beacn12pjwc

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 6, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, more...

integer, non-monotonic, +, A000005

a(n)=τ(n)
τ(n)=number of divisors of n
n≥1
2 operations
Prime
a(n)=Ω(floor(2^τ(n)))
τ(n)=number of divisors of n
Ω(n)=max distinct factors of n
n≥1
6 operations
Prime
a(n)=τ(n*p(n))/2
p(n)=nth prime
τ(n)=number of divisors of n
n≥1
7 operations
Prime

Sequence gekakw1rgdk0j

1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 19, 2, 3, 2, 23, 2, 5, 2, 3, 2, 29, 2, 31, 2, 3, 2, 5, 2, 37, 2, 3, 2, 41, 2, 43, 2, 3, 2, 47, 2, 7, 2, more...

integer, non-monotonic, +, A020639

a(n)=lpf(n)
lpf(n)=least prime factor of n
n≥1
2 operations
Prime
a(n)=gcd(n, lpf(n))
lpf(n)=least prime factor of n
gcd(a,b)=greatest common divisor
n≥1
4 operations
Prime
a(n)=gpf(lpf(n)²)
lpf(n)=least prime factor of n
gpf(n)=greatest prime factor of n
n≥1
4 operations
Prime
a(n)=exp(Λ(lpf(n)))
lpf(n)=least prime factor of n
Λ(n)=Von Mangoldt's function
n≥1
4 operations
Prime

Sequence qxbjop1xs1vff

1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, 2, 17, 3, 19, 5, 7, 11, 23, 3, 5, 13, 3, 7, 29, 5, 31, 2, 11, 17, 7, 3, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 3, 7, 5, more...

integer, non-monotonic, +, A006530

a(n)=gpf(n)
gpf(n)=greatest prime factor of n
n≥1
2 operations
Prime
a(n)=gcd(n, gpf(n))
gpf(n)=greatest prime factor of n
gcd(a,b)=greatest common divisor
n≥1
4 operations
Prime
a(n)=lpf(gpf(n)²)
gpf(n)=greatest prime factor of n
lpf(n)=least prime factor of n
n≥1
4 operations
Prime
a(n)=exp(Λ(gpf(n)))
gpf(n)=greatest prime factor of n
Λ(n)=Von Mangoldt's function
n≥1
4 operations
Prime
a(n)=floor(sqrt(floor(gpf(n)²)))
gpf(n)=greatest prime factor of n
n≥1
6 operations
Prime

Sequence wqwhagpwcscgc

1, 6, 1, 8, 0, 3, 3, 9, 8, 8, 7, 4, 9, 8, 9, 4, 8, 4, 8, 2, 0, 4, 5, 8, 6, 8, 3, 4, 3, 6, 5, 6, 3, 8, 1, 1, 7, 7, 2, 0, 3, 0, 9, 1, 7, 9, 8, 0, 5, 7, more...

integer, non-monotonic, +, A001622

a(n)=de[ϕ]
ϕ=1.618... (Golden Ratio)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant
a(n)=de[sqrt(1+ϕ)]
ϕ=1.618... (Golden Ratio)
de(a)=decimal expansion of a
n≥0
5 operations
Power
a(n)=de[2*5*ϕ]
ϕ=1.618... (Golden Ratio)
de(a)=decimal expansion of a
n≥0
6 operations
Arithmetic

Sequence dodcahtwj3i1g

2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, 1, 1, 16, 1, 1, 18, 1, 1, 20, 1, 1, 22, 1, 1, 24, 1, 1, 26, 1, 1, 28, 1, 1, 30, 1, 1, 32, 1, 1, more...

integer, non-monotonic, +, A003417

a(n)=contfrac[e]
e=2.7182... (Euler e)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant
a(n)=contfrac[root(log(2), 2)]
root(n,a)=the n-th root of a
contfrac(a)=continued fraction of a
n≥0
5 operations
Power

Sequence l2ff0du3kwl3n

2, 1.4142135623730951, 1.189207115002721, 1.0905077326652577, 1.0442737824274138, 1.0218971486541166, 1.0108892860517005, 1.0054299011128027, 1.0027112750502025, 1.0013547198921082, 1.0006771306930664, 1.0003385080526823, 1.0001692397053021, 1.0000846162726942, 1.0000423072413958, 1.0000211533969647, 1.0000105766425498, 1.0000052883072919, 1.0000026441501502, 1.0000013220742012, 1.0000006610368821, 1.0000003305183864, 1.0000001652591797, 1.0000000826295865, 1.0000000413147925, more...

decimal, strictly-monotonic, convergent, +

a(n)=sqrt(a(n-1))
a(0)=2
n≥0
2 operations
Recursive
a(n)=root(4, a(n-1)²)
a(0)=2
root(n,a)=the n-th root of a
n≥0
4 operations
Recursive
a(n)=a(n-1)^(1/2)
a(0)=2
n≥0
5 operations
Recursive

Sequence 3obzf0s451s5l

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, more...

integer, strictly-monotonic, +, A000040

a(n)=p(n)
p(n)=nth prime
n≥1
2 operations
Prime
a(n)=gpf(floor(2*p(n)))
p(n)=nth prime
gpf(n)=greatest prime factor of n
n≥1
6 operations
Prime

Sequence idcen5jpa2zpc

2, 7, 1, 8, 2, 8, 1, 8, 2, 8, 4, 5, 9, 0, 4, 5, 2, 3, 5, 3, 6, 0, 2, 8, 7, 4, 7, 1, 3, 5, 2, 6, 6, 2, 4, 9, 7, 7, 5, 7, 2, 4, 7, 0, 9, 3, 6, 9, 9, 9, more...

integer, non-monotonic, +, A001113

a(n)=de[e]
e=2.7182... (Euler e)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant
a(n)=de[root(log(2), 2)]
root(n,a)=the n-th root of a
de(a)=decimal expansion of a
n≥0
5 operations
Power
a(n)=de[2*5*e]
e=2.7182... (Euler e)
de(a)=decimal expansion of a
n≥0
6 operations
Arithmetic

Sequence xecz0440luoph

3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8, 8, 4, 1, 9, 7, 1, 6, 9, 3, 9, 9, 3, 7, 5, 1, more...

integer, non-monotonic, +, A000796

a(n)=de[π]
π=3.1415... (Pi)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant
a(n)=de[acos(-1)]
de(a)=decimal expansion of a
n≥0
4 operations
Trigonometric
a(n)=de[exp(abs(log(π)))]
π=3.1415... (Pi)
de(a)=decimal expansion of a
n≥0
5 operations
Power
a(n)=de[2*5*π]
π=3.1415... (Pi)
de(a)=decimal expansion of a
n≥0
6 operations
Arithmetic

Sequence 45e5bvr3z2z3c

3, 1.7320508075688772, 1.3160740129524924, 1.147202690439877, 1.0710754830729146, 1.0349277670798647, 1.0173139963058921, 1.0086198472694716, 1.0043006757288733, 1.0021480308461785, 1.0010734392871377, 1.000536575686835, 1.0002682518638863, 1.0001341169382667, 1.000067056220865, 1.0000335275483843, 1.0000167636336825, 1.000008381781714, 1.0000041908820754, 1.0000020954388422, 1.0000010477188723, 1.000000523859299, 1.0000002619296153, 1.000000130964799, 1.0000000654823973, more...

decimal, strictly-monotonic, convergent, +

a(n)=sqrt(a(n-1))
a(0)=3
n≥0
2 operations
Recursive
a(n)=root(4, a(n-1)²)
a(0)=3
root(n,a)=the n-th root of a
n≥0
4 operations
Recursive
a(n)=a(n-1)^(1/2)
a(0)=3
n≥0
5 operations
Recursive

Sequence gw2idni12ytnj

3, 5, 11, 31, 127, 709, 5381, 52711, 648391, more...

integer, strictly-monotonic, +

a(n)=p(a(n-1))
a(0)=3
p(n)=nth prime
n≥0
2 operations
Prime
a(n)=or(1, p(a(n-1)))
a(0)=3
p(n)=nth prime
or(a,b)=bitwise or
n≥0
4 operations
Prime

Sequence dc212nwugb3uj

3, 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3, 13, 1, 4, 2, 6, 6, 99, 1, 2, 2, 6, 3, 5, 1, 1, 6, 8, 1, 7, 1, 2, 3, 7, more...

integer, non-monotonic, +, A001203

a(n)=contfrac[π]
π=3.1415... (Pi)
contfrac(a)=continued fraction of a
n≥0
2 operations
DecimalConstant
a(n)=contfrac[acos(-1)]
contfrac(a)=continued fraction of a
n≥0
4 operations
Trigonometric
a(n)=contfrac[exp(abs(log(π)))]
π=3.1415... (Pi)
contfrac(a)=continued fraction of a
n≥0
5 operations
Power

Sequence teeygcg3imnnl

4, 2, 1.4142135623730951, 1.189207115002721, 1.0905077326652577, 1.0442737824274138, 1.0218971486541166, 1.0108892860517005, 1.0054299011128027, 1.0027112750502025, 1.0013547198921082, 1.0006771306930664, 1.0003385080526823, 1.0001692397053021, 1.0000846162726942, 1.0000423072413958, 1.0000211533969647, 1.0000105766425498, 1.0000052883072919, 1.0000026441501502, 1.0000013220742012, 1.0000006610368821, 1.0000003305183864, 1.0000001652591797, 1.0000000826295865, more...

decimal, strictly-monotonic, convergent, +

a(n)=sqrt(a(n-1))
a(0)=4
n≥0
2 operations
Recursive
a(n)=root(4, a(n-1)²)
a(0)=4
root(n,a)=the n-th root of a
n≥0
4 operations
Recursive
a(n)=a(n-1)^(1/2)
a(0)=4
n≥0
5 operations
Recursive

Sequence zlrqnubjy5rce

4, 7, 17, 59, 277, 1787, 15299, 167449, 2269733, more...

integer, strictly-monotonic, +, A057450

a(n)=p(a(n-1))
a(0)=4
p(n)=nth prime
n≥0
2 operations
Prime
a(n)=or(1, p(a(n-1)))
a(0)=4
p(n)=nth prime
or(a,b)=bitwise or
n≥0
4 operations
Prime

Sequence bo2mhitgs5rxi

5, 2.23606797749979, 1.4953487812212205, 1.2228445449938519, 1.1058230170302352, 1.0515811984959769, 1.0254663322098765, 1.0126531154397722, 1.006306670672401, 1.0031483791904372, 1.0015729525054264, 1.0007861672232619, 1.0003930063846218, 1.0001964838893516, 1.00009823711941, 1.0000491173534478, 1.000024558375167, 1.0000122791121953, 1.0000061395372506, 1.0000030697639135, 1.000001534880779, 1.000000767440095, 1.0000003837199738, 1.0000001918599686, 1.0000000959299797, more...

decimal, strictly-monotonic, convergent, +

a(n)=sqrt(a(n-1))
a(0)=5
n≥0
2 operations
Recursive
a(n)=root(4/2, a(n-1))
a(0)=5
root(n,a)=the n-th root of a
n≥0
5 operations
Recursive
a(n)=a(n-1)^(1/2)
a(0)=5
n≥0
5 operations
Recursive
a(n)=exp(log(a(n-1))/2)
a(0)=5
n≥0
5 operations
Recursive

Sequence qvvnqvlyivqen

5, 6, 7, 1, 4, 3, 2, 9, 0, 4, 0, 9, 7, 8, 3, 8, 7, 2, 9, 9, 9, 9, 6, 8, 6, 6, 2, 2, 1, 0, 3, 5, 5, 5, 4, 9, 7, 5, 3, 8, 1, 5, 7, 8, 7, 1, 8, 6, 5, 1, more...

integer, non-monotonic, +, A030178

a(n)=de[W1]
W1=0.5671... (Lambert W)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant
a(n)=de[log(W1)]
W1=0.5671... (Lambert W)
de(a)=decimal expansion of a
n≥0
3 operations
Power

Sequence tz5ztfhojkiqe

5, 6, 12, 28, 56, 120, 360, 1170, 3276, 10192, 24738, 61440, more...

integer, strictly-monotonic, +, A051572

a(n)=σ(a(n-1))
a(0)=5
σ(n)=divisor sum of n
n≥0
2 operations
Prime
a(n)=lcm(σ(a(n-1)), 2)
a(0)=5
σ(n)=divisor sum of n
lcm(a,b)=least common multiple
n≥0
4 operations
Prime

Sequence knd2jdmkw4tcn

5, 7, 7, 2, 1, 5, 6, 6, 4, 9, 0, 1, 5, 3, 2, 8, 6, 0, 6, 0, 6, 5, 1, 2, 0, 9, 0, 0, 8, 2, 4, 0, 2, 4, 3, 1, 0, 4, 2, 1, 5, 9, 3, 3, 5, 9, 3, 9, 9, 2, more...

integer, non-monotonic, +, A001620

a(n)=de[γ]
γ=0.5772... (Euler Gamma)
de(a)=decimal expansion of a
n≥0
2 operations
DecimalConstant
a(n)=de[2*5*γ]
γ=0.5772... (Euler Gamma)
de(a)=decimal expansion of a
n≥0
6 operations
Arithmetic
a(n)=de[(γ/sqrt(γ))²]
γ=0.5772... (Euler Gamma)
de(a)=decimal expansion of a
n≥0
6 operations
Power

Sequence gjavorx3phgp

5, 11, 31, 127, 709, 5381, 52711, 648391, more...

integer, strictly-monotonic, +

a(n)=p(a(n-1))
a(0)=5
p(n)=nth prime
n≥0
2 operations
Prime
a(n)=or(1, p(a(n-1)))
a(0)=5
p(n)=nth prime
or(a,b)=bitwise or
n≥0
4 operations
Prime

Sequence alv0irdpu3yyj

-2, 0, 1, -1, 2, -2, 1, 0, 1, -2, 1, -1, 2, 0, -1, -1, 1, -1, 1, 1, 0, -2, 1, 0, 1, -1, 0, -1, 0, 0, 1, 1, 0, 0, -1, -1, 2, 0, -1, -1, 0, 0, 1, 0, 1, -2, 1, 0, 0, 1, more...

integer, non-monotonic, +-, A127440

a(n)=Δ[μ(n)]
μ(n)=Möbius function
Δ(a)=differences of a
n≥1
3 operations
Prime
a(n)=Δ[floor(exp(μ(n)))]
μ(n)=Möbius function
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence j5d5yp1t1kr4k

-2, 0, 2, -2, 2, -2, 0, 2, 0, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 2, 0, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, 0, 0, 2, -2, 0, 2, -2, 2, more...

integer, non-monotonic, +-

a(n)=Δ[λ(n)]
λ(n)=Liouville's function
Δ(a)=differences of a
n≥1
3 operations
Prime
a(n)=Δ[xor(1, λ(n))]
λ(n)=Liouville's function
xor(a,b)=bitwise exclusive or
Δ(a)=differences of a
n≥1
5 operations
Prime
a(n)=Δ[or(1, λ(n))]
λ(n)=Liouville's function
or(a,b)=bitwise or
Δ(a)=differences of a
n≥1
5 operations
Prime
a(n)=Δ[floor(exp(λ(n)))]
λ(n)=Liouville's function
Δ(a)=differences of a
n≥1
5 operations
Prime

Sequence g2mm2we1holzd

-2, 3, -3, 4, 4, -7, 4, -1, -2, 2, 3, 1, -2, 2, -6, -1, 1, 5, -4, 2, -4, 4, -2, -1, 0, 5, -5, -1, 5, 2, -4, -5, 2, 6, 0, -4, -3, 8, -2, -6, 5, 3, -6, 6, 0, -6, 4, -2, -4, more...

integer, non-monotonic, +-, A095916

a(n)=Δ[de[π]]
π=3.1415... (Pi)
de(a)=decimal expansion of a
Δ(a)=differences of a
n≥0
3 operations
DecimalConstant
a(n)=Δ[1+de[π]]
π=3.1415... (Pi)
de(a)=decimal expansion of a
Δ(a)=differences of a
n≥0
5 operations
Arithmetic

Sequence eticauab1kot

-1, -2, -3, -2, -5, -3, -7, -2, -3, -5, -11, -3, -13, -7, -5, -2, -17, -3, -19, -5, -7, -11, -23, -3, -5, -13, -3, -7, -29, -5, -31, -2, -11, -17, -7, -3, -37, -19, -13, -5, -41, -7, -43, -11, -5, -23, -47, -3, -7, -5, more...

integer, non-monotonic, -

a(n)=-gpf(n)
gpf(n)=greatest prime factor of n
n≥1
3 operations
Prime
a(n)=-gpf(φ(n²))
ϕ(n)=number of relative primes (Euler's totient)
gpf(n)=greatest prime factor of n
n≥1
5 operations
Prime

Sequence vdw5rsi1esttn

-1, -2, -2, -3, -2, -4, -2, -4, -3, -4, -2, -6, -2, -4, -4, -5, -2, -6, -2, -6, -4, -4, -2, -8, -3, -4, -4, -6, -2, -8, -2, -6, -4, -4, -4, -9, -2, -4, -4, -8, -2, -8, -2, -6, -6, -4, -2, -10, -3, -6, more...

integer, non-monotonic, -

a(n)=-τ(n)
τ(n)=number of divisors of n
n≥1
3 operations
Prime
a(n)=log(1/exp(τ(n)))
τ(n)=number of divisors of n
n≥1
6 operations
Prime

Sequence 0dndnbzf4olfo

-1, -1, -2, -6, -24, -120, -720, -5040, -40320, -362880, -3628800, -39916800, -479001600, -6227020800, -87178291200, -1307674368000, -20922789888000, -355687428096000, more...

integer, monotonic, -

a(n)=-n!
n≥0
3 operations
Combinatoric
a(n)=-∏[C(n, a(n-1))]
a(0)=1
C(n,k)=binomial coefficient
∏(a)=partial products of a
n≥0
5 operations
Combinatoric
a(n)=∏[floor(n-2/n)]
∏(a)=partial products of a
n≥1
7 operations
Arithmetic

Sequence oyhxazizrszjh

-1, 1, -1, 0, 3, -3, 0, 5, -5, 0, 7, -7, 0, 9, -9, 0, 11, -11, 0, 13, -13, 0, 15, -15, 0, 17, -17, 0, 19, -19, 0, 21, -21, 0, 23, -23, 0, 25, -25, 0, 27, -27, 0, 29, -29, 0, 31, -31, 0, more...

integer, non-monotonic, +-

a(n)=Δ[contfrac[e]]
e=2.7182... (Euler e)
contfrac(a)=continued fraction of a
Δ(a)=differences of a
n≥0
3 operations
DecimalConstant
a(n)=Δ[1+contfrac[e]]
e=2.7182... (Euler e)
contfrac(a)=continued fraction of a
Δ(a)=differences of a
n≥0
5 operations
Arithmetic

Sequence sgowcwxdfg2qm

-1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, more...

integer, non-monotonic, +-

a(n)=-λ(n)
λ(n)=Liouville's function
n≥1
3 operations
Prime
a(n)=xor(-2, λ(n))
λ(n)=Liouville's function
xor(a,b)=bitwise exclusive or
n≥1
5 operations
Prime
a(n)=μ(2+λ(n))
λ(n)=Liouville's function
μ(n)=Möbius function
n≥1
5 operations
Prime

Sequence tweyw4wkgff2f

-1, 1, 1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 1, -1, -1, 0, 1, 0, 1, 0, -1, -1, 1, 0, 0, -1, 0, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, -1, -1, 0, 1, 1, 1, 0, 0, -1, 1, 0, 0, 0, more...

integer, non-monotonic, +-

a(n)=-μ(n)
μ(n)=Möbius function
n≥1
3 operations
Prime
a(n)=log(1/exp(μ(n)))
μ(n)=Möbius function
n≥1
6 operations
Prime

Sequence hg4p5djg1ejjl

-1, 2, -6, 24, -120, 720, -5040, 40320, -362880, 3628800, -39916800, 479001600, -6227020800, 87178291200, -1307674368000, 20922789888000, -355687428096000, more...

integer, non-monotonic, +-

a(n)=∏[-n]
∏(a)=partial products of a
n≥1
3 operations
Arithmetic
a(n)=∏[xor(n, -1)]
xor(a,b)=bitwise exclusive or
∏(a)=partial products of a
n≥0
5 operations
Bitwise
a(n)=∏[Δ[a(n-1)-n]]
a(0)=1
Δ(a)=differences of a
∏(a)=partial products of a
n≥0
5 operations
Recursive

Sequence oenvlrha0zxcb

-0.7853981633974483, -0.32175055439664213, -0.14189705460416402, -0.07677189126977813, -0.04758310327698334, -0.032246882435253976, -0.02325162281046289, -0.01754206005740233, -0.013697773372865818, -0.01098856868273379, -0.00900876529041672, -0.00751865531230389, -0.006369340618663344, -0.005464426484487639, -0.004739301009466512, -0.004149353779866471, -0.003662987280234731, -0.003257317470005683, -0.002915443634775139, -0.002624665888999012, -0.002375292444959376, -0.002159823855406362, -0.001972384030046292, -0.001808316292942314, -0.001663891975298482, more...

decimal, strictly-monotonic, convergent, -

a(n)=Δ[acot(n)]
Δ(a)=differences of a
n≥0
3 operations
Trigonometric
a(n)=Δ[atan(-n)]
Δ(a)=differences of a
n≥0
4 operations
Trigonometric

Sequence llkyrrajh4rze

0, -1, -4, -9, -16, -25, -36, -49, -64, -81, -100, -121, -144, -169, -196, -225, -256, -289, -324, -361, -400, -441, -484, -529, -576, -625, -676, -729, -784, -841, -900, -961, -1024, -1089, -1156, -1225, -1296, -1369, -1444, -1521, -1600, -1681, -1764, -1849, -1936, -2025, -2116, -2209, -2304, -2401, more...

integer, strictly-monotonic, -

a(n)=-n²
n≥0
3 operations
Power
a(n)=n*floor(-n)
n≥0
5 operations
Arithmetic
a(n)=a(n-1)-Δ[n²]
a(0)=0
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=∑[or(1, a(n-1)-2)]
a(0)=0
or(a,b)=bitwise or
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=n-lcm(1+n, n)
lcm(a,b)=least common multiple
n≥0
7 operations
Divisibility

Sequence 3narje4d4nqjh

0, -1, -3, -6, -10, -15, -21, -28, -36, -45, -55, -66, -78, -91, -105, -120, -136, -153, -171, -190, -210, -231, -253, -276, -300, -325, -351, -378, -406, -435, -465, -496, -528, -561, -595, -630, -666, -703, -741, -780, -820, -861, -903, -946, -990, -1035, -1081, -1128, -1176, -1225, more...

integer, strictly-monotonic, -

a(n)=∑[-n]
∑(a)=partial sums of a
n≥0
3 operations
Arithmetic
a(n)=a(n-1)-n
a(0)=0
n≥0
3 operations
Recursive
a(n)=-∑[C(n, a(n-1))]
a(0)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑[floor(log(2)-n)]
∑(a)=partial sums of a
n≥0
6 operations
Power
a(n)=∑[λ(n²)-n]
λ(n)=Liouville's function
∑(a)=partial sums of a
n≥1
6 operations
Prime

Sequence qobrounzmgbon

0, -1, -1, -2, -1, -3, -2, -3, -1, -4, -3, -5, -2, -5, -3, -4, -1, -5, -4, -7, -3, -8, -5, -7, -2, -7, -5, -8, -3, -7, -4, -5, -1, -6, -5, -9, -4, -11, -7, -10, -3, -11, -8, -13, -5, -12, -7, -9, -2, -9, more...

integer, non-monotonic, -

a(n)=-stern(n)
stern(n)=Stern-Brocot sequence
n≥0
3 operations
Recursive
a(n)=a(n-1)-Δ[stern(n)]
a(0)=0
stern(n)=Stern-Brocot sequence
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence 0bratltk3sv0l

0, -1, -1, -2, -1, -2, -1, -3, -2, -2, -1, -3, -1, -2, -2, -4, -1, -3, -1, -3, -2, -2, -1, -4, -2, -2, -3, -3, -1, -3, -1, -5, -2, -2, -2, -4, -1, -2, -2, -4, -1, -3, -1, -3, -3, -2, -1, -5, -2, -3, more...

integer, non-monotonic, -

a(n)=-Ω(n)
Ω(n)=max distinct factors of n
n≥1
3 operations
Prime
a(n)=log(1/exp(Ω(n)))
Ω(n)=max distinct factors of n
n≥1
6 operations
Prime
a(n)=1-Ω(n*p(n))
p(n)=nth prime
Ω(n)=max distinct factors of n
n≥1
7 operations
Prime

Sequence vpyfixzgwq2bf

0, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, -1, -1, more...

integer, non-monotonic, -, A000493

a(n)=floor(sin(n))
n≥0
3 operations
Trigonometric
a(n)=floor(atan(sin(n)))
n≥0
4 operations
Trigonometric
a(n)=floor(tanh(sin(n)))
n≥0
4 operations
Trigonometric

Sequence wgvcgyzlgpf2f

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, more...

integer, monotonic, +

a(n)=floor(tanh(n))
n≥0
3 operations
Trigonometric
a(n)=floor(sqrt(tanh(n)))
n≥0
4 operations
Trigonometric
a(n)=floor(log(n)/3)
n≥1
5 operations
Power
a(n)=log2(pt(ceil(log(n))))
pt(n)=Pascals triangle by rows
n≥1
5 operations
Combinatoric
a(n)=Ω(pt(ceil(log(n))))
pt(n)=Pascals triangle by rows
Ω(n)=max distinct factors of n
n≥1
5 operations
Prime

Sequence kjumfr24fbm3i

0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16, 24, 24, 24, 24, 24, 24, 24, 24, 32, 32, 32, 32, 32, 32, 32, 32, 40, 40, 40, 40, 40, 40, 40, 40, 48, 48, more...

integer, monotonic, +

a(n)=and(56, n)
and(a,b)=bitwise and
n≥0
3 operations
Bitwise
a(n)=n-n%8
n≥0
5 operations
Divisibility

Sequence 2gawxcdjflree

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +

a(n)=char[p(a(n-1))]
a(0)=5
p(n)=nth prime
char(a)=characteristic function of a (in range)
n≥0
3 operations
Prime
a(n)=char[or(1, p(a(n-1)))]
a(0)=5
p(n)=nth prime
or(a,b)=bitwise or
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[gpf(∏[p(a(n-1))])]
a(0)=5
p(n)=nth prime
∏(a)=partial products of a
gpf(n)=greatest prime factor of n
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[lpf(p(a(n-1))²)]
a(0)=5
p(n)=nth prime
lpf(n)=least prime factor of n
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[exp(Λ(p(a(n-1))))]
a(0)=5
p(n)=nth prime
Λ(n)=Von Mangoldt's function
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime

Sequence wsp1p31jbz0cp

0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +

a(n)=char[σ(a(n-1))]
a(0)=5
σ(n)=divisor sum of n
char(a)=characteristic function of a (in range)
n≥0
3 operations
Prime
a(n)=char[or(4, σ(a(n-1)))]
a(0)=5
σ(n)=divisor sum of n
or(a,b)=bitwise or
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[lcm(σ(a(n-1)), 2)]
a(0)=5
σ(n)=divisor sum of n
lcm(a,b)=least common multiple
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime

Sequence f3rkhfvw2vmjh

0, 0, 0, 0, 0.6931471805599453, 0, 0, 1.0986122886681098, 1.0986122886681098, 0, 0, 1.3862943611198906, 1.791759469228055, 1.3862943611198906, 0, 0, 1.6094379124341003, 2.302585092994046, 2.302585092994046, 1.6094379124341003, 0, 0, 1.791759469228055, 2.70805020110221, 2.995732273553991, more...

decimal, non-monotonic, +

a(n)=log(pt(n))
pt(n)=Pascals triangle by rows
n≥0
3 operations
Combinatoric
a(n)=log(pt(n)²)/2
pt(n)=Pascals triangle by rows
n≥0
6 operations
Combinatoric

Sequence esfaxj45cqu0h

0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +

a(n)=char[p(a(n-1))]
a(0)=4
p(n)=nth prime
char(a)=characteristic function of a (in range)
n≥0
3 operations
Prime
a(n)=char[2+P(a(n-1))]
a(0)=4
P(n)=partition numbers
char(a)=characteristic function of a (in range)
n≥0
5 operations
Combinatoric
a(n)=char[or(1, p(a(n-1)))]
a(0)=4
p(n)=nth prime
or(a,b)=bitwise or
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[round(exp(log2(a(n-1))))]
a(0)=4
char(a)=characteristic function of a (in range)
n≥0
5 operations
Recursive
a(n)=char[gpf(p(a(n-1))²)]
a(0)=4
p(n)=nth prime
gpf(n)=greatest prime factor of n
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime

Sequence i03tmuqhhdjeg

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +

a(n)=char[σ(a(n-1))]
a(0)=4
σ(n)=divisor sum of n
char(a)=characteristic function of a (in range)
n≥0
3 operations
Prime
a(n)=char[lcm(n, σ(a(n-1)))]
a(0)=4
σ(n)=divisor sum of n
lcm(a,b)=least common multiple
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime

Sequence bdicsyvtm5hmd

0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 8, 8, 12, 12, 12, 12, 16, 16, 16, 16, 20, 20, 20, 20, 24, 24, 24, 24, 28, 28, 28, 28, 32, 32, 32, 32, 36, 36, 36, 36, 40, 40, 40, 40, 44, 44, 44, 44, 48, 48, more...

integer, monotonic, +

a(n)=and(60, n)
and(a,b)=bitwise and
n≥0
3 operations
Bitwise
a(n)=n-n%4
n≥0
5 operations
Divisibility

Sequence ob4wf4100avbh

0, 0, 0, 0.6931471805599453, 0, 0, 0, 1.0986122886681098, 0.6931471805599453, 0, 0, 0.6931471805599453, 0, 0, 0, 1.6094379124341003, 0, 0.6931471805599453, 0, 0.6931471805599453, 0, 0, 0, 1.0986122886681098, 0.6931471805599453, more...

decimal, non-monotonic, +

a(n)=log(agc(n))
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
3 operations
Prime
a(n)=Λ(agc(n))
agc(n)=number of factorizations into prime powers (abelian group count)
Λ(n)=Von Mangoldt's function
n≥0
3 operations
Prime

Sequence ioywxzo1cwifc

0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, more...

integer, non-monotonic, +, A056170

a(n)=Ω(agc(n))
agc(n)=number of factorizations into prime powers (abelian group count)
Ω(n)=max distinct factors of n
n≥0
3 operations
Prime
a(n)=τ(agc(n))-1
agc(n)=number of factorizations into prime powers (abelian group count)
τ(n)=number of divisors of n
n≥0
5 operations
Prime
a(n)=ceil(log(τ(agc(n))))
agc(n)=number of factorizations into prime powers (abelian group count)
τ(n)=number of divisors of n
n≥0
5 operations
Prime
a(n)=ceil(log2(τ(agc(n))))
agc(n)=number of factorizations into prime powers (abelian group count)
τ(n)=number of divisors of n
n≥0
5 operations
Prime
a(n)=ceil(Λ(τ(agc(n))))
agc(n)=number of factorizations into prime powers (abelian group count)
τ(n)=number of divisors of n
Λ(n)=Von Mangoldt's function
n≥0
5 operations
Prime

Sequence bzzcjrdswzryf

0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +

a(n)=char[catalan(a(n-1))]
a(0)=3
catalan(n)=the catalan numbers
char(a)=characteristic function of a (in range)
n≥0
3 operations
Combinatoric
a(n)=char[or(n, catalan(a(n-1)))]
a(0)=3
catalan(n)=the catalan numbers
or(a,b)=bitwise or
char(a)=characteristic function of a (in range)
n≥0
5 operations
Combinatoric
a(n)=char[lcm(n, catalan(a(n-1)))]
a(0)=3
catalan(n)=the catalan numbers
lcm(a,b)=least common multiple
char(a)=characteristic function of a (in range)
n≥0
5 operations
Combinatoric
a(n)=char[P(φ(p(a(n-1))))]
a(0)=3
p(n)=nth prime
ϕ(n)=number of relative primes (Euler's totient)
P(n)=partition numbers
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime

Sequence tvsw3dtw3wg4p

0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +

a(n)=char[p(a(n-1))]
a(0)=3
p(n)=nth prime
char(a)=characteristic function of a (in range)
n≥0
3 operations
Prime
a(n)=char[or(1, p(a(n-1)))]
a(0)=3
p(n)=nth prime
or(a,b)=bitwise or
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[gpf(∏[p(a(n-1))])]
a(0)=3
p(n)=nth prime
∏(a)=partial products of a
gpf(n)=greatest prime factor of n
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[lpf(p(a(n-1))²)]
a(0)=3
p(n)=nth prime
lpf(n)=least prime factor of n
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[exp(Λ(p(a(n-1))))]
a(0)=3
p(n)=nth prime
Λ(n)=Von Mangoldt's function
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime

Sequence 1f15nnnsxrjae

0, 0, 0.6931471805599453, 0, 0.6931471805599453, 0, 1.0986122886681098, 0.6931471805599453, 0.6931471805599453, 0, 1.0986122886681098, 0, 0.6931471805599453, 0.6931471805599453, 0.6931471805599453, 0, 1.0986122886681098, 0, 1.0986122886681098, 0.6931471805599453, 0.6931471805599453, 0, 0.6931471805599453, 0.6931471805599453, 0.6931471805599453, more...

decimal, non-monotonic, +

a(n)=Λ(Ω(n))
Ω(n)=max distinct factors of n
Λ(n)=Von Mangoldt's function
n≥2
3 operations
Prime
a(n)=log(gpf(Ω(n)))
Ω(n)=max distinct factors of n
gpf(n)=greatest prime factor of n
n≥2
4 operations
Prime

Sequence jp2ml154op4rc

0, 0, 0.6931471805599453, 0, 0.6931471805599453, 0, 1.0986122886681098, 0.6931471805599453, 0.6931471805599453, 0, 1.0986122886681098, 0, 0.6931471805599453, 0.6931471805599453, 1.3862943611198906, 0, 1.0986122886681098, 0, 1.0986122886681098, 0.6931471805599453, 0.6931471805599453, 0, 1.3862943611198906, 0.6931471805599453, 0.6931471805599453, more...

decimal, non-monotonic, +

a(n)=log(Ω(n))
Ω(n)=max distinct factors of n
n≥2
3 operations
Prime
a(n)=log(Ω(n)²)/2
Ω(n)=max distinct factors of n
n≥2
6 operations
Prime

Sequence vlsnf3zjnoc1o

0, 0, 0.6931471805599453, 0, 1.0986122886681098, 0.6931471805599453, 1.0986122886681098, 0, 0.6931471805599453, 1.0986122886681098, 1.6094379124341003, 0.6931471805599453, 1.6094379124341003, 1.0986122886681098, 0.6931471805599453, 0, 1.6094379124341003, 0.6931471805599453, 1.9459101490553132, 1.0986122886681098, 0.6931471805599453, 1.6094379124341003, 1.9459101490553132, 0.6931471805599453, 1.9459101490553132, more...

decimal, non-monotonic, +

a(n)=Λ(stern(n))
stern(n)=Stern-Brocot sequence
Λ(n)=Von Mangoldt's function
n≥1
3 operations
Prime
a(n)=log(gpf(stern(n)))
stern(n)=Stern-Brocot sequence
gpf(n)=greatest prime factor of n
n≥1
4 operations
Prime

Sequence rdjsgcvdpt4l

0, 0, 0.6931471805599453, 0.6931471805599453, 1.3862943611198906, 0.6931471805599453, 1.791759469228055, 1.3862943611198906, 1.791759469228055, 1.3862943611198906, 2.302585092994046, 1.3862943611198906, 2.4849066497880004, 1.791759469228055, 2.0794415416798357, 2.0794415416798357, 2.772588722239781, 1.791759469228055, 2.8903717578961645, 2.0794415416798357, 2.4849066497880004, 2.302585092994046, 3.091042453358316, 2.0794415416798357, 2.995732273553991, more...

decimal, non-monotonic, +

a(n)=log(φ(n))
ϕ(n)=number of relative primes (Euler's totient)
n≥1
3 operations
Prime
a(n)=log(φ(n)²)/2
ϕ(n)=number of relative primes (Euler's totient)
n≥1
6 operations
Prime

Sequence gkvra3qav4mme

0, 0, 0.6931471805599453, 1.0986122886681098, 1.6094379124341003, 1.9459101490553132, 2.3978952727983707, 2.70805020110221, 3.091042453358316, 3.4011973816621555, 3.7376696182833684, 4.02535169073515, 4.343805421853684, 4.61512051684126, 4.90527477843843, 5.170483995038151, 5.442417710521793, 5.6937321388027, 5.953243334287785, 6.194405391104672, 6.440946540632921, 6.674561391814426, 6.90975328164481, 7.134890851565884, 7.362010551259734, more...

decimal, monotonic, +

a(n)=log(P(n))
P(n)=partition numbers
n≥0
3 operations
Combinatoric
a(n)=log(P(n)²)/2
P(n)=partition numbers
n≥0
6 operations
Combinatoric

Sequence fjjehs5q3qphf

0, 0, 1, -1, 0, 0, 2, -1, -1, 0, 1, -1, 0, 0, 4, -4, 1, -1, 1, -1, 0, 0, 2, -1, -1, 2, -1, -1, 0, 0, 6, -6, 0, 0, 3, -3, 0, 0, 2, -2, 0, 0, 1, 0, -1, 0, 4, -3, 0, -1, more...

integer, non-monotonic, +-

a(n)=Δ[agc(n)]
agc(n)=number of factorizations into prime powers (abelian group count)
Δ(a)=differences of a
n≥0
3 operations
Prime
a(n)=Δ[and(7, agc(n))]
agc(n)=number of factorizations into prime powers (abelian group count)
and(a,b)=bitwise and
Δ(a)=differences of a
n≥0
5 operations
Prime
a(n)=Δ[xor(8, agc(n))]
agc(n)=number of factorizations into prime powers (abelian group count)
xor(a,b)=bitwise exclusive or
Δ(a)=differences of a
n≥0
5 operations
Prime
a(n)=Δ[or(8, agc(n))]
agc(n)=number of factorizations into prime powers (abelian group count)
or(a,b)=bitwise or
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence 3uwynzcum1xlo

0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +

a(n)=char[a(n-1)²]
a(0)=2
char(a)=characteristic function of a (in range)
n≥0
3 operations
Recursive
a(n)=char[a(n-1)^a(n-2)]
a(0)=2
a(1)=2
char(a)=characteristic function of a (in range)
n≥0
4 operations
Recursive
a(n)=char[2^φ(n)]
ϕ(n)=number of relative primes (Euler's totient)
char(a)=characteristic function of a (in range)
n≥1
5 operations
Prime
a(n)=char[2+catalan(a(n-1))]
a(0)=2
catalan(n)=the catalan numbers
char(a)=characteristic function of a (in range)
n≥0
5 operations
Combinatoric
a(n)=char[lcm(a(n-1)², 2)]
a(0)=2
lcm(a,b)=least common multiple
char(a)=characteristic function of a (in range)
n≥0
5 operations
Recursive

Sequence clahvkolobpsp

0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, more...

integer, non-monotonic, +

a(n)=Ω(Ω(n))
Ω(n)=max distinct factors of n
n≥2
3 operations
Prime
a(n)=stern(Ω(n)-1)
Ω(n)=max distinct factors of n
stern(n)=Stern-Brocot sequence
n≥2
5 operations
Prime
a(n)=ceil(log(τ(Ω(n))))
Ω(n)=max distinct factors of n
τ(n)=number of divisors of n
n≥2
5 operations
Prime
a(n)=ceil(log2(τ(Ω(n))))
Ω(n)=max distinct factors of n
τ(n)=number of divisors of n
n≥2
5 operations
Prime
a(n)=ceil(Λ(τ(Ω(n))))
Ω(n)=max distinct factors of n
τ(n)=number of divisors of n
Λ(n)=Von Mangoldt's function
n≥2
5 operations
Prime

Sequence vigfmh33tzdcd

0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +

a(n)=char[p(a(n-1))]
a(0)=2
p(n)=nth prime
char(a)=characteristic function of a (in range)
n≥0
3 operations
Prime
a(n)=char[or(1, p(a(n-1)))]
a(0)=2
p(n)=nth prime
or(a,b)=bitwise or
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[gpf(∏[p(a(n-1))])]
a(0)=2
p(n)=nth prime
∏(a)=partial products of a
gpf(n)=greatest prime factor of n
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[lpf(p(a(n-1))²)]
a(0)=2
p(n)=nth prime
lpf(n)=least prime factor of n
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[exp(Λ(p(a(n-1))))]
a(0)=2
p(n)=nth prime
Λ(n)=Von Mangoldt's function
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime

Sequence ncdwvmpwwmitd

0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, more...

integer, non-monotonic, +

a(n)=char[p(n)]
p(n)=nth prime
char(a)=characteristic function of a (in range)
n≥1
3 operations
Prime
a(n)=char[gpf(2+n)]
gpf(n)=greatest prime factor of n
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[lpf(2+n)]
lpf(n)=least prime factor of n
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[exp(Λ(p(n)))]
p(n)=nth prime
Λ(n)=Von Mangoldt's function
char(a)=characteristic function of a (in range)
n≥1
5 operations
Prime

Sequence nhj1lolwivgs

0, 0, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 4, 3, 4, 3, 4, 4, 4, 3, 3, 3, 4, 2, 2, 4, 3, 3, more...

integer, non-monotonic, +

a(n)=Ω(φ(n))
ϕ(n)=number of relative primes (Euler's totient)
Ω(n)=max distinct factors of n
n≥1
3 operations
Prime
a(n)=Ω(φ(n)²)/2
ϕ(n)=number of relative primes (Euler's totient)
Ω(n)=max distinct factors of n
n≥1
6 operations
Prime

Sequence yi4rbbpqzb14e

0, 0, 1, 1, 2, 3, 4, 3, 4, 4, 5, more...

integer, non-monotonic, +, A081399

a(n)=Ω(catalan(n))
catalan(n)=the catalan numbers
Ω(n)=max distinct factors of n
n≥0
3 operations
Prime
a(n)=ceil(log2(τ(catalan(n))))
catalan(n)=the catalan numbers
τ(n)=number of divisors of n
n≥0
5 operations
Prime

Sequence texjg1xckplrb

0, 0, 2, 2, 4, 4, 6, 6, 8, 8, 10, 10, 12, 12, 14, 14, 16, 16, 18, 18, 20, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 32, 32, 34, 34, 36, 36, 38, 38, 40, 40, 42, 42, 44, 44, 46, 46, 48, 48, more...

integer, monotonic, +, A052928

a(n)=and(62, n)
and(a,b)=bitwise and
n≥0
3 operations
Bitwise
a(n)=n-n%2
n≥0
5 operations
Divisibility
a(n)=gcd(a(n-1), 2)+a(n-2)
a(0)=0
a(1)=0
gcd(a,b)=greatest common divisor
n≥0
5 operations
Recursive
a(n)=2*floor(n/2)
n≥0
6 operations
Arithmetic
a(n)=n-and(1, n)²
and(a,b)=bitwise and
n≥0
6 operations
Power

Sequence bcuhcgiplv5dj

0, 0.027777777777777776, 0.05555555555555555, 0.08333333333333333, 0.1111111111111111, 0.1388888888888889, 0.16666666666666666, 0.19444444444444445, 0.2222222222222222, 0.25, 0.2777777777777778, 0.3055555555555556, 0.3333333333333333, 0.3611111111111111, 0.3888888888888889, 0.4166666666666667, 0.4444444444444444, 0.4722222222222222, 0.5, 0.5277777777777778, 0.5555555555555556, 0.5833333333333334, 0.6111111111111112, 0.6388888888888888, 0.6666666666666666, more...

decimal, strictly-monotonic, +

a(n)=n/36
n≥0
3 operations
Arithmetic
a(n)=n/de[2/3]²
de(a)=decimal expansion of a
n≥0
7 operations
Power

Sequence etctgba41dgxj

0, 0.037037037037037035, 0.07407407407407407, 0.1111111111111111, 0.14814814814814814, 0.18518518518518517, 0.2222222222222222, 0.25925925925925924, 0.2962962962962963, 0.3333333333333333, 0.37037037037037035, 0.4074074074074074, 0.4444444444444444, 0.48148148148148145, 0.5185185185185185, 0.5555555555555556, 0.5925925925925926, 0.6296296296296297, 0.6666666666666666, 0.7037037037037037, 0.7407407407407407, 0.7777777777777778, 0.8148148148148148, 0.8518518518518519, 0.8888888888888888, more...

decimal, strictly-monotonic, +

a(n)=n/27
n≥0
3 operations
Arithmetic
a(n)=n/root(1/3, 3)
root(n,a)=the n-th root of a
n≥0
7 operations
Power

Sequence dqyfxumwbk2dd

0, 0.1111111111111111, 0.2222222222222222, 0.3333333333333333, 0.4444444444444444, 0.5555555555555556, 0.6666666666666666, 0.7777777777777778, 0.8888888888888888, 1, 1.1111111111111112, 1.2222222222222223, 1.3333333333333333, 1.4444444444444444, 1.5555555555555556, 1.6666666666666667, 1.7777777777777777, 1.8888888888888888, 2, 2.111111111111111, 2.2222222222222223, 2.3333333333333335, 2.4444444444444446, 2.5555555555555554, 2.6666666666666665, more...

decimal, strictly-monotonic, +

a(n)=n/9
n≥0
3 operations
Arithmetic
a(n)=n/root(1/2, 3)
root(n,a)=the n-th root of a
n≥0
7 operations
Power

Sequence xzfxxexeq3dpc

0, 0.3333333333333333, 0.6666666666666666, 1, 1.3333333333333333, 1.6666666666666667, 2, 2.3333333333333335, 2.6666666666666665, 3, 3.3333333333333335, 3.6666666666666665, 4, 4.333333333333333, 4.666666666666667, 5, 5.333333333333333, 5.666666666666667, 6, 6.333333333333333, 6.666666666666667, 7, 7.333333333333333, 7.666666666666667, 8, more...

decimal, strictly-monotonic, +

a(n)=n/3
n≥0
3 operations
Arithmetic
a(n)=gcd(n, n²)/3
gcd(a,b)=greatest common divisor
n≥0
6 operations
Power
a(n)=n/Δ[3+a(n-1)]
a(0)=1
Δ(a)=differences of a
n≥0
6 operations
Recursive
a(n)=gcd(2*n, n)/3
gcd(a,b)=greatest common divisor
n≥0
7 operations
Divisibility
a(n)=(n-λ(n²))/3
λ(n)=Liouville's function
n≥1
7 operations
Prime

Sequence swptftqsnqn2b

0, 0.6931471805599453, 0.6931471805599453, 1.0986122886681098, 0.6931471805599453, 1.3862943611198906, 0.6931471805599453, 1.3862943611198906, 1.0986122886681098, 1.3862943611198906, 0.6931471805599453, 1.791759469228055, 0.6931471805599453, 1.3862943611198906, 1.3862943611198906, 1.6094379124341003, 0.6931471805599453, 1.791759469228055, 0.6931471805599453, 1.791759469228055, 1.3862943611198906, 1.3862943611198906, 0.6931471805599453, 2.0794415416798357, 1.0986122886681098, more...

decimal, non-monotonic, +

a(n)=log(τ(n))
τ(n)=number of divisors of n
n≥1
3 operations
Prime
a(n)=log(τ(n)²)/2
τ(n)=number of divisors of n
n≥1
6 operations
Prime

Sequence zgxzry00zfmmk

0, 0.6931471805599453, 1.0986122886681098, 0.6931471805599453, 1.6094379124341003, 0.6931471805599453, 1.9459101490553132, 0.6931471805599453, 1.0986122886681098, 0.6931471805599453, 2.3978952727983707, 0.6931471805599453, 2.5649493574615367, 0.6931471805599453, 1.0986122886681098, 0.6931471805599453, 2.833213344056216, 0.6931471805599453, 2.9444389791664403, 0.6931471805599453, 1.0986122886681098, 0.6931471805599453, 3.1354942159291497, 0.6931471805599453, 1.6094379124341003, more...

decimal, non-monotonic, +

a(n)=log(lpf(n))
lpf(n)=least prime factor of n
n≥1
3 operations
Prime
a(n)=Λ(lpf(n))
lpf(n)=least prime factor of n
Λ(n)=Von Mangoldt's function
n≥1
3 operations
Prime

Sequence 54kgbtpqjxucc

0, 0.6931471805599453, 1.0986122886681098, 0.6931471805599453, 1.6094379124341003, 1.0986122886681098, 1.9459101490553132, 0.6931471805599453, 1.0986122886681098, 1.6094379124341003, 2.3978952727983707, 1.0986122886681098, 2.5649493574615367, 1.9459101490553132, 1.6094379124341003, 0.6931471805599453, 2.833213344056216, 1.0986122886681098, 2.9444389791664403, 1.6094379124341003, 1.9459101490553132, 2.3978952727983707, 3.1354942159291497, 1.0986122886681098, 1.6094379124341003, more...

decimal, non-monotonic, +

a(n)=log(gpf(n))
gpf(n)=greatest prime factor of n
n≥1
3 operations
Prime
a(n)=Λ(gpf(n))
gpf(n)=greatest prime factor of n
Λ(n)=Von Mangoldt's function
n≥1
3 operations
Prime
a(n)=log(gpf(n)²)/2
gpf(n)=greatest prime factor of n
n≥1
6 operations
Prime

Sequence mg5illw2ayefh

0, 0.6931471805599453, 1.791759469228055, 3.1780538303479453, 4.787491742782046, 6.579251212010101, 8.525161361065415, 10.60460290274525, 12.80182748008147, 15.104412573075518, 17.502307845873887, 19.98721449566189, 22.552163853123425, 25.191221182738683, 27.899271383840894, 30.671860106080675, 33.50507345013689, 36.39544520803305, 39.339884187199495, 42.335616460753485, 45.38013889847691, 48.47118135183523, 51.60667556776438, 54.784729398112326, 58.003605222980525, more...

decimal, strictly-monotonic, +

a(n)=∑[log(n)]
∑(a)=partial sums of a
n≥1
3 operations
Power
a(n)=log(1+n)+a(n-1)
a(0)=0
n≥0
6 operations
Recursive

Sequence 3f3eclphdhemg

0, 0.8325546111576977, 1.048147073968205, 0.8325546111576977, 1.2686362411795196, 0, 1.3949588341794583, 0.8325546111576977, 1.048147073968205, 0, 1.5485138917033876, 0, 1.6015459273656616, 0, 0, 0.8325546111576977, 1.6832151805566085, 0, 1.71593676432625, 0, 0, 0, 1.7707326777153998, 0, 1.2686362411795196, more...

decimal, non-monotonic, +

a(n)=sqrt(Λ(n))
Λ(n)=Von Mangoldt's function
n≥1
3 operations
Prime
a(n)=root(4, Λ(n)²)
Λ(n)=Von Mangoldt's function
root(n,a)=the n-th root of a
n≥1
5 operations
Prime

Sequence d34sgmm3ciujd

0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, more...

integer, non-monotonic, +-, A000494

a(n)=round(sin(n))
n≥0
3 operations
Trigonometric
a(n)=round(sinh(sin(n)))
n≥0
4 operations
Trigonometric

Sequence fgp0ok4naz01c

0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +, A316341

a(n)=char[n!]
char(a)=characteristic function of a (in range)
n≥0
3 operations
Combinatoric
a(n)=char[n*a(n-1)]
a(0)=1
char(a)=characteristic function of a (in range)
n≥0
4 operations
Recursive
a(n)=char[pt(n)!]
pt(n)=Pascals triangle by rows
char(a)=characteristic function of a (in range)
n≥0
4 operations
Combinatoric
a(n)=char[τ(n)!]
τ(n)=number of divisors of n
char(a)=characteristic function of a (in range)
n≥1
4 operations
Prime
a(n)=char[Ω(n)!]
Ω(n)=max distinct factors of n
char(a)=characteristic function of a (in range)
n≥1
4 operations
Prime

Sequence cq3vwjywkevzj

0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, more...

integer, non-monotonic, +

a(n)=ceil(sin(n))
n≥0
3 operations
Trigonometric
a(n)=ceil(atan(sin(n)))
n≥0
4 operations
Trigonometric
a(n)=ceil(tanh(sin(n)))
n≥0
4 operations
Trigonometric

Sequence kyac2yropktci

0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, non-monotonic, +

a(n)=char[p(a(n-1))]
a(0)=1
p(n)=nth prime
char(a)=characteristic function of a (in range)
n≥0
3 operations
Prime
a(n)=char[or(a(n-3), p(a(n-1)))]
a(0)=1
a(1)=2
a(2)=3
p(n)=nth prime
or(a,b)=bitwise or
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[gpf(∏[p(a(n-1))])]
a(0)=1
p(n)=nth prime
∏(a)=partial products of a
gpf(n)=greatest prime factor of n
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[lpf(p(a(n-1))²)]
a(0)=1
p(n)=nth prime
lpf(n)=least prime factor of n
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime
a(n)=char[exp(Λ(p(a(n-1))))]
a(0)=1
p(n)=nth prime
Λ(n)=Von Mangoldt's function
char(a)=characteristic function of a (in range)
n≥0
5 operations
Prime

Sequence yngoua0myhull

0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, more...

integer, non-monotonic, +

a(n)=char[gpf(n)]
gpf(n)=greatest prime factor of n
char(a)=characteristic function of a (in range)
n≥1
3 operations
Prime
a(n)=char[lpf(n)]
lpf(n)=least prime factor of n
char(a)=characteristic function of a (in range)
n≥1
3 operations
Prime
a(n)=char[exp(Λ(n))]
Λ(n)=Von Mangoldt's function
char(a)=characteristic function of a (in range)
n≥1
4 operations
Prime
a(n)=and(1, char[lpf(n)])
lpf(n)=least prime factor of n
char(a)=characteristic function of a (in range)
and(a,b)=bitwise and
n≥1
5 operations
Prime
a(n)=root(3, char[lpf(n)])
lpf(n)=least prime factor of n
char(a)=characteristic function of a (in range)
root(n,a)=the n-th root of a
n≥1
5 operations
Prime

Sequence bkdps0gk2kari

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, more...

integer, monotonic, +

a(n)=round(atan(n))
n≥0
3 operations
Trigonometric
a(n)=floor(sqrt(log2(n)))
n≥1
4 operations
Power
a(n)=stern(ceil(log2(log2(n))))
stern(n)=Stern-Brocot sequence
n≥2
5 operations
Recursive

Sequence rpvg23ohf1d3c

0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 3, 1, 2, more...

integer, non-monotonic, +

a(n)=stern(Ω(n))
Ω(n)=max distinct factors of n
stern(n)=Stern-Brocot sequence
n≥1
3 operations
Prime
a(n)=Ω(σ(2^Ω(n)))
Ω(n)=max distinct factors of n
σ(n)=divisor sum of n
n≥1
6 operations
Prime

Sequence tktdnownr02cc

0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 2, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, more...

integer, non-monotonic, +, A058061

a(n)=Ω(τ(n))
τ(n)=number of divisors of n
Ω(n)=max distinct factors of n
n≥1
3 operations
Prime
a(n)=Ω(τ(n)²)/2
τ(n)=number of divisors of n
Ω(n)=max distinct factors of n
n≥1
6 operations
Prime

Sequence qlf3d40uqfgeb

0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, more...

integer, monotonic, +, A000196

a(n)=floor(sqrt(n))
n≥0
3 operations
Power
a(n)=∑[char[pt(n)²]]
pt(n)=Pascals triangle by rows
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑[char[∑[2+a(n-1)]]]
a(0)=1
∑(a)=partial sums of a
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive
a(n)=τ(n)%2+a(n-1)
a(0)=0
τ(n)=number of divisors of n
n≥0
6 operations
Prime

Sequence s5a53utdww13n

0, 1, 1, 1.4142135623730951, 1, 1.4142135623730951, 1, 1.7320508075688772, 1.4142135623730951, 1.4142135623730951, 1, 1.7320508075688772, 1, 1.4142135623730951, 1.4142135623730951, 2, 1, 1.7320508075688772, 1, 1.7320508075688772, 1.4142135623730951, 1.4142135623730951, 1, 2, 1.4142135623730951, more...

decimal, non-monotonic, +

a(n)=sqrt(Ω(n))
Ω(n)=max distinct factors of n
n≥1
3 operations
Prime
a(n)=root(4, Ω(n)²)
Ω(n)=max distinct factors of n
root(n,a)=the n-th root of a
n≥1
5 operations
Prime
a(n)=Ω(n)^(1/2)
Ω(n)=max distinct factors of n
n≥1
6 operations
Prime

Sequence hnxruzbvips0k

0, 1, 1, 1.4142135623730951, 1, 1.7320508075688772, 1.4142135623730951, 1.7320508075688772, 1, 2, 1.7320508075688772, 2.23606797749979, 1.4142135623730951, 2.23606797749979, 1.7320508075688772, 2, 1, 2.23606797749979, 2, 2.6457513110645907, 1.7320508075688772, 2.8284271247461903, 2.23606797749979, 2.6457513110645907, 1.4142135623730951, more...

decimal, non-monotonic, +

a(n)=sqrt(stern(n))
stern(n)=Stern-Brocot sequence
n≥0
3 operations
Recursive
a(n)=root(4, stern(n)²)
stern(n)=Stern-Brocot sequence
root(n,a)=the n-th root of a
n≥0
5 operations
Recursive

Sequence kzpxgr055fwee

0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, more...

integer, monotonic, +, A000523

a(n)=floor(log2(n))
n≥1
3 operations
Power
a(n)=∑[char[or(n, a(n-1))]]
a(0)=1
or(a,b)=bitwise or
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[char[∑[2*a(n-1)]]]
a(0)=1
∑(a)=partial sums of a
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive

Sequence uth5s1sdppb4g

0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, more...

integer, monotonic, +, A000194

a(n)=round(sqrt(n))
n≥0
3 operations
Power
a(n)=char[n+n²]+a(n-1)
a(0)=0
char(a)=characteristic function of a (in range)
n≥0
7 operations
Recursive

Sequence nfg4ocm1ms2ao

0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, more...

integer, monotonic, +, A110654

a(n)=n-a(n-1)
a(0)=0
n≥0
3 operations
Recursive
a(n)=ceil(n/2)
n≥0
4 operations
Arithmetic
a(n)=∑[and(1, n)]
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
4 operations
Bitwise
a(n)=∑[xor(1, a(n-1))]
a(0)=0
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=round(sinh(log(n)))
n≥1
4 operations
Trigonometric

Sequence qpmqbompmh1hn

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903, 2971215073, 4807526976, 7778742049, more...

integer, monotonic, +, A000045

a(n)=a(n-1)+a(n-2)
a(0)=0
a(1)=1
n≥0
3 operations
Recursive
a(n)=2*a(n-1)-a(n-3)
a(0)=0
a(1)=1
a(2)=1
n≥0
5 operations
Recursive

Sequence ela0apdjovjqo

0, 1, 1, 4, 1, 4, 1, 9, 4, 4, 1, 9, 1, 4, 4, 16, 1, 9, 1, 9, 4, 4, 1, 16, 4, 4, 9, 9, 1, 9, 1, 25, 4, 4, 4, 16, 1, 4, 4, 16, 1, 9, 1, 9, 9, 4, 1, 25, 4, 9, more...

integer, non-monotonic, +

a(n)=Ω(n)²
Ω(n)=max distinct factors of n
n≥1
3 operations
Prime
a(n)=sqrt(Ω(n)^4)
Ω(n)=max distinct factors of n
n≥1
5 operations
Prime
a(n)=Ω(n%p(n²))²
p(n)=nth prime
Ω(n)=max distinct factors of n
n≥1
7 operations
Prime
a(n)=Ω(gpf(n)^Ω(n))²
gpf(n)=greatest prime factor of n
Ω(n)=max distinct factors of n
n≥1
7 operations
Prime

Sequence y2rfmpcmhzu2h

0, 1, 1, 4, 1, 9, 4, 9, 1, 16, 9, 25, 4, 25, 9, 16, 1, 25, 16, 49, 9, 64, 25, 49, 4, 49, 25, 64, 9, 49, 16, 25, 1, 36, 25, 81, 16, 121, 49, 100, 9, 121, 64, 169, 25, 144, 49, 81, 4, 81, more...

integer, non-monotonic, +

a(n)=stern(n)²
stern(n)=Stern-Brocot sequence
n≥0
3 operations
Recursive
a(n)=sqrt(stern(n)^4)
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Recursive

Sequence vihefww4t2xvg

0, 1, 2, 1, 2, 3, 3, 2, 1, 3, 3, 3, 2, 4, 4, 1, 3, 2, 3, 3, 5, 4, 4, 4, 1, 3, 4, 4, 3, 5, 5, 3, 5, 4, 5, 2, 2, 4, 4, 4, 3, 6, 3, 4, 3, 5, 5, 3, 2, 2, more...

integer, non-monotonic, +, A058063

a(n)=Ω(σ(n))
σ(n)=divisor sum of n
Ω(n)=max distinct factors of n
n≥1
3 operations
Prime
a(n)=Ω(σ(n)²)/2
σ(n)=divisor sum of n
Ω(n)=max distinct factors of n
n≥1
6 operations
Prime

Sequence gwyogtngbtfxf

0, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, more...

integer, monotonic, +, A135034

a(n)=ceil(sqrt(n))
n≥0
3 operations
Power
a(n)=char[n²]+a(n-1)
a(0)=0
char(a)=characteristic function of a (in range)
n≥0
5 operations
Recursive
a(n)=char[∑[a(n-2)]²]+a(n-1)
a(0)=0
a(1)=1
∑(a)=partial sums of a
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive

Sequence 5nkup5uykhmpj

0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, more...

integer, monotonic, +, A029837

a(n)=ceil(log2(n))
n≥1
3 operations
Power
a(n)=∑[char[2*a(n-1)]]
a(0)=1
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[char[a(n-1)²/a(n-2)]]
a(0)=1
a(1)=2
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence 0guw2gjud0avi

0, 1, 2, 3, 1, 6, 3, 1, 1, 2, 1, 1, 1, 1, 3, 10, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 3, 1, 13, 7, 4, 1, 1, 1, 7, 2, 4, 1, 1, 2, 5, 14, 1, 10, 1, 4, 2, 18, 3, 1, more...

integer, non-monotonic, +, A016730

a(n)=contfrac[log(2)]
contfrac(a)=continued fraction of a
n≥0
3 operations
Power
a(n)=contfrac[Λ(2^n)]
Λ(n)=Von Mangoldt's function
contfrac(a)=continued fraction of a
n≥1
5 operations
Prime

Sequence 3jaam2mtj5ded

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, more...

integer, non-monotonic, +

a(n)=n%30
n≥0
3 operations
Divisibility
a(n)=n%∏[stern(a(n-1))]
a(0)=5
stern(n)=Stern-Brocot sequence
∏(a)=partial products of a
n≥0
5 operations
Recursive

Sequence ejbhk5wjuaulo

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, more...

integer, non-monotonic, +

a(n)=and(31, n)
and(a,b)=bitwise and
n≥0
3 operations
Bitwise
a(n)=n%32
n≥0
3 operations
Divisibility

Sequence wmoj5d5xh3vll

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, more...

integer, non-monotonic, +

a(n)=n%40
n≥0
3 operations
Divisibility
a(n)=n%∏[φ(a(n-1))]
a(0)=5
ϕ(n)=number of relative primes (Euler's totient)
∏(a)=partial products of a
n≥0
5 operations
Prime

[0] [1] [2] [3] [4] ... [305]