Sequence Database

A database with 951925 machine generated integer and decimal sequences.

Displaying result 0-99 of total 529800. [0] [1] [2] [3] [4] ... [5297]

Sequence 42rfwqvyrnhlj

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, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, more...

integer, strictly-monotonic, +, A001477

a(n)=n
n≥0
1 operation
Variable
a(n)=1+a(n-1)
a(0)=0
n≥0
3 operations
Recursive
a(n)=n%50
n≥0
3 operations
Divisibility
a(n)=(2-1)*n
n≥0
5 operations
Arithmetic
a(n)=n^(2-1)
n≥0
5 operations
Power
a(n)=C(n, a(n-1))
a(0)=0
C(n,k)=binomial coefficient
n≥0
3 operations
Combinatoric
a(n)=∑(agc(a(n-1)))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
3 operations
Prime
a(n)=∑(ceil(cos(a(n-1))))
a(0)=0
∑(a)=partial sums of a
n≥0
4 operations
Trigonometric

Sequence buqmnzuccjoq

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

integer, constant, monotonic, A000004

a(n)=a(n-1)
a(0)=0
n≥0
1 operation
Recursive

Sequence dgbv3olkf3toh

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, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, more...

integer, strictly-monotonic, -, A001489

a(n)=-n
n≥0
2 operations
Arithmetic
a(n)=a(n-1)-1
a(0)=0
n≥0
3 operations
Recursive
a(n)=(1-n)%n
n≥1
5 operations
Divisibility
a(n)=-sqrt(n*n)
n≥0
5 operations
Power
a(n)=-C(n, -a(n-1))
a(0)=0
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=λ(n²)-n
λ(n)=Liouville's function
n≥1
5 operations
Prime

Sequence arfihgdbhmbdh

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
Arithmetic
a(n)=lcm(n, n²)
lcm(a,b)=least common multiple
n≥0
4 operations
Divisibility
a(n)=n^(1+1)
n≥0
5 operations
Power
a(n)=(1-∑(a(n-1)))²
a(0)=1
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑(a(n-1)!)²
a(0)=0
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=∑(agc(a(n-1)))²
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
4 operations
Prime

Sequence tedqmvzugfstb

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, +, A002487

a(n)=stern(n)
stern(n)=Stern-Brocot sequence
n≥0
2 operations
Recursive
a(n)=stern(lcm(n, 2))
lcm(a,b)=least common multiple
stern(n)=Stern-Brocot sequence
n≥0
4 operations
Divisibility
a(n)=stern(sqrt(n*n))
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Power
a(n)=stern(∑(a(n-1)!))
a(0)=0
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
4 operations
Combinatoric
a(n)=stern(∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
4 operations
Prime

Sequence vtsqmvu022mjo

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)=∑(gcd(n, n²))
gcd(a,b)=greatest common divisor
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑(sqrt(n*n))
∑(a)=partial sums of a
n≥0
5 operations
Power
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)=∑(∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
4 operations
Prime

Sequence dqjfnt5tdtf1p

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, periodic-2, non-monotonic, +-, A033999

a(n)=-a(n-1)
a(0)=1
n≥0
2 operations
Recursive
a(n)=(-1)^n
n≥0
4 operations
Power
a(n)=cos(π*n)
π=3.141...
n≥0
4 operations
Trigonometric
a(n)=-a(n-1)%2
a(0)=1
n≥0
4 operations
Divisibility
a(n)=-∏(Δ(-n))
Δ(a)=differences of a
∏(a)=partial products of a
n≥0
5 operations
Arithmetic
a(n)=Δ((2/a(n-1))!)
a(0)=1
Δ(a)=differences of a
n≥0
5 operations
Combinatoric

Sequence xw3as224tu2qo

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

integer, periodic-2, non-monotonic, +-

a(n)=-a(n-1)
a(0)=2
n≥0
2 operations
Recursive
a(n)=round(tan(a(n-1)))
a(0)=2
n≥0
3 operations
Trigonometric
a(n)=-a(n-1)%3
a(0)=2
n≥0
4 operations
Divisibility
a(n)=(1-2)^n*2
n≥0
7 operations
Power
a(n)=∏(-C(a(n-1), 2))
a(0)=2
C(n,k)=binomial coefficient
∏(a)=partial products of a
n≥0
5 operations
Combinatoric

Sequence hfwl31yaewfw

2, 4, 16, 256, 65536, 4294967296, more...

integer, strictly-monotonic, +, A001146

a(n)=a(n-1)²
a(0)=2
n≥0
2 operations
Recursive
a(n)=a(n-1)^(1+1)
a(0)=2
n≥0
5 operations
Power
a(n)=lcm(a(n-1), 2)²
a(0)=2
lcm(a,b)=least common multiple
n≥0
4 operations
Divisibility
a(n)=C(a(n-1), Δ(n))²
a(0)=2
Δ(a)=differences of a
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=(λ(n)*a(n-1))²
a(0)=2
λ(n)=Liouville's function
n≥0
5 operations
Prime

Sequence yv3fppyevpgxk

3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, 3, -3, more...

integer, periodic-2, non-monotonic, +-, A174971

a(n)=-a(n-1)
a(0)=3
n≥0
2 operations
Recursive
a(n)=∏((-1)^a(n-1))
a(0)=3
∏(a)=partial products of a
n≥0
5 operations
Power
a(n)=-a(n-1)%4
a(0)=3
n≥0
4 operations
Divisibility
a(n)=∏(-C(a(n-1), 3))
a(0)=3
C(n,k)=binomial coefficient
∏(a)=partial products of a
n≥0
5 operations
Combinatoric

Sequence lpylbs2ffxw3k

3, 9, 81, 6561, 43046721, more...

integer, strictly-monotonic, +, A011764

a(n)=a(n-1)²
a(0)=3
n≥0
2 operations
Recursive
a(n)=lcm(a(n-1), 3)²
a(0)=3
lcm(a,b)=least common multiple
n≥0
4 operations
Divisibility
a(n)=a(n-1)^(1+1)
a(0)=3
n≥0
5 operations
Power
a(n)=9^Ω(a(n-1))
a(0)=3
Ω(n)=max factorization terms
n≥0
4 operations
Prime
a(n)=C(a(n-1), Δ(n))²
a(0)=3
Δ(a)=differences of a
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric

Sequence zefx4n0mxnbln

4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, more...

integer, periodic-2, non-monotonic, +-

a(n)=-a(n-1)
a(0)=4
n≥0
2 operations
Recursive
a(n)=-a(n-1)%5
a(0)=4
n≥0
4 operations
Divisibility
a(n)=log(Δ(n))-a(n-1)
a(0)=4
Δ(a)=differences of a
n≥0
5 operations
Power
a(n)=∏(-C(a(n-1), 4))
a(0)=4
C(n,k)=binomial coefficient
∏(a)=partial products of a
n≥0
5 operations
Combinatoric
a(n)=∏(floor(sin(a(n-1))))
a(0)=4
∏(a)=partial products of a
n≥0
4 operations
Trigonometric

Sequence vusq2s4v30qyc

4, 16, 256, 65536, 4294967296, more...

integer, strictly-monotonic, +

a(n)=a(n-1)²
a(0)=4
n≥0
2 operations
Recursive
a(n)=a(n-1)^(1+1)
a(0)=4
n≥0
5 operations
Power
a(n)=lcm(a(n-1), 2)²
a(0)=4
lcm(a,b)=least common multiple
n≥0
4 operations
Divisibility
a(n)=C(a(n-1), Δ(n))²
a(0)=4
Δ(a)=differences of a
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=(λ(n)*a(n-1))²
a(0)=4
λ(n)=Liouville's function
n≥0
5 operations
Prime

Sequence s1ae2qzrjrsul

5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, more...

integer, periodic-2, non-monotonic, +-

a(n)=-a(n-1)
a(0)=5
n≥0
2 operations
Recursive
a(n)=-a(n-1)%6
a(0)=5
n≥0
4 operations
Divisibility
a(n)=∏((-1)^a(n-1))
a(0)=5
∏(a)=partial products of a
n≥0
5 operations
Power
a(n)=∏(-C(a(n-1), 5))
a(0)=5
C(n,k)=binomial coefficient
∏(a)=partial products of a
n≥0
5 operations
Combinatoric
a(n)=∏(floor(sin(a(n-1))))
a(0)=5
∏(a)=partial products of a
n≥0
4 operations
Trigonometric

Sequence dwrbbizvnafqp

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
Arithmetic
a(n)=-lcm(n, n²)
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=a(n-1)-Δ(n²)
a(0)=0
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=-sqrt(n^4)
n≥0
5 operations
Power
a(n)=-∑(a(n-1)!)²
a(0)=0
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=-∑(agc(a(n-1)))²
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence shr3uhqxjwpwk

0, 0.6931471806, 1.0986122887, 1.3862943611, 1.6094379124, 1.7917594692, 1.9459101491, 2.0794415417, 2.1972245773, 2.302585093, 2.3978952728, 2.4849066498, 2.5649493575, 2.6390573296, 2.7080502011, 2.7725887222, 2.8332133441, 2.8903717579, 2.9444389792, 2.9957322736, 3.0445224377, 3.0910424534, 3.1354942159, 3.1780538303, 3.2188758249, more...

decimal, strictly-monotonic, +

a(n)=log(n)
n≥1
2 operations
Power
a(n)=log(∑(composite(a(n-1))))
a(0)=1
composite(n)=nth composite number
∑(a)=partial sums of a
n≥0
4 operations
Prime
a(n)=log(∑(a(n-1)!))
a(0)=1
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric

Sequence rgxae4yi3xabd

0, 1, 1.4142135624, 1.7320508076, 2, 2.2360679775, 2.4494897428, 2.6457513111, 2.8284271247, 3, 3.1622776602, 3.3166247904, 3.4641016151, 3.6055512755, 3.7416573868, 3.8729833462, 4, 4.1231056256, 4.2426406871, 4.3588989435, 4.472135955, 4.582575695, 4.6904157598, 4.7958315233, 4.8989794856, more...

decimal, strictly-monotonic, +

a(n)=sqrt(n)
n≥0
2 operations
Power
a(n)=sqrt(∑(a(n-1)!))
a(0)=0
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=sqrt(∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
4 operations
Prime

Sequence co5f4i13hchai

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

integer, monotonic, +, A000142

a(n)=n*a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=n!
n≥0
2 operations
Combinatoric
a(n)=lcm(n, n*a(n-1))
a(0)=1
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=n^(2-1)*a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=a(n-1)*∑(composite(a(n-1)))
a(0)=1
composite(n)=nth composite number
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence 3sjiabcajvvtd

1, 2.7182818285, 7.3890560989, 20.0855369232, 54.5981500331, 148.4131591026, 403.4287934927, 1096.6331584285, 2980.9579870417, 8103.0839275754, 22026.4657948067, 59874.1417151978, 162754.7914190039, 442413.3920089205, 1202604.2841647768, 3269017.3724721107, 8886110.520507872, 24154952.7535753, 65659969.13733051, 178482300.96318725, 485165195.4097903, 1318815734.4832146, 3584912846.131592, 9744803446.248903, 26489122129.84347, more...

decimal, strictly-monotonic, +

a(n)=exp(n)
n≥0
2 operations
Power
a(n)=exp(∑(a(n-1)!))
a(0)=0
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=exp(∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
4 operations
Prime

Sequence umplcbnlhplyn

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)=a(n-1)-n
a(0)=0
n≥0
3 operations
Recursive
a(n)=∑(-n)
∑(a)=partial sums of a
n≥0
3 operations
Arithmetic
a(n)=a(n-1)^(2-1)-n
a(0)=0
n≥0
7 operations
Power
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)=a(n-1)-n%(1+n)
a(0)=0
n≥0
7 operations
Divisibility
a(n)=∑(-∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence hkbamxejiornm

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)=-stern(lcm(n, 2))
lcm(a,b)=least common multiple
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Divisibility
a(n)=-stern(∑(a(n-1)!))
a(0)=0
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Combinatoric
a(n)=-stern(∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Prime

Sequence dnb1wejvpehll

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)=n%2+a(n-1)
a(0)=0
n≥0
5 operations
Divisibility
a(n)=∑(sqrt(1-a(n-1)))
a(0)=0
∑(a)=partial sums of a
n≥0
5 operations
Power
a(n)=C(n-a(n-1), a(n-2))
a(0)=0
a(1)=1
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=∑(floor(cos(a(n-1))))
a(0)=0
∑(a)=partial sums of a
n≥0
4 operations
Trigonometric
a(n)=∑(Ω(2-a(n-1)))
a(0)=0
Ω(n)=max factorization terms
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence ml10wnhgjogxe

0, 1, 1, 4, 1, 7, 4, 9, 1, 14, 7, 13, 4, 29, 9, 16, 1, 23, 14, 43, 7, 36, 13, 29, 4, 43, 29, 64, 9, 67, 16, 25, 1, 34, 23, 89, 14, 115, 43, 46, 7, 85, 36, 79, 13, 46, 29, 79, 4, 97, more...

integer, non-monotonic, +, A286387

a(n)=stern(n²)
stern(n)=Stern-Brocot sequence
n≥0
3 operations
Recursive
a(n)=stern(lcm(n, 2)²)
lcm(a,b)=least common multiple
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Divisibility
a(n)=stern(sqrt(n^4))
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Power
a(n)=stern(∑(a(n-1)!)²)
a(0)=0
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Combinatoric
a(n)=stern(∑(agc(a(n-1)))²)
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Prime

Sequence fu2oreb5xmtgg

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)=stern(lcm(n, 2))²
lcm(a,b)=least common multiple
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Divisibility
a(n)=sqrt(stern(n)^4)
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Power
a(n)=stern(∑(a(n-1)!))²
a(0)=0
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Combinatoric
a(n)=stern(∑(agc(a(n-1))))²
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Prime

Sequence hndi1jkl020kk

1, 0, -2, -5, -9, -14, -20, -27, -35, -44, -54, -65, -77, -90, -104, -119, -135, -152, -170, -189, -209, -230, -252, -275, -299, -324, -350, -377, -405, -434, -464, -495, -527, -560, -594, -629, -665, -702, -740, -779, -819, -860, -902, -945, -989, -1034, -1080, -1127, -1175, -1224, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=1
n≥0
3 operations
Recursive
a(n)=1-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=a(n-1)^(2-1)-n
a(0)=1
n≥0
7 operations
Power
a(n)=a(n-1)-n%(1+n)
a(0)=1
n≥0
7 operations
Divisibility
a(n)=a(n-1)-∑(a(n-1)!)
a(0)=1
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=a(n-1)-∑(composite(a(n-1)))
a(0)=1
composite(n)=nth composite number
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence spwfakucb0xrj

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

integer, non-monotonic, +, A028242

a(n)=n-a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=n%(1+n)-a(n-1)
a(0)=1
n≥0
7 operations
Divisibility
a(n)=C(n-a(n-1), a(n-2))
a(0)=1
a(1)=0
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=n^(2-1)-a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=agc(Δ(a(n-1)))+a(n-2)
a(0)=1
a(1)=0
Δ(a)=differences of a
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence ict5nshkayqre

1, 1, 0.5, 0.1666666667, 0.0416666667, 0.0083333333, 0.0013888889, 0.0001984127, 0.0000248016, 0.0000027557, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

decimal, monotonic, +

a(n)=a(n-1)/n
a(0)=1
n≥0
3 operations
Recursive
a(n)=n^(1-2)*a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=a(n-1)/n%(1+n)
a(0)=1
n≥0
7 operations
Divisibility
a(n)=a(n-1)/∑(a(n-1)!)
a(0)=1
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=a(n-1)/∑(composite(a(n-1)))
a(0)=1
composite(n)=nth composite number
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence f444dv54iouae

1, 1, 2, 1.5, 2.6666666667, 1.875, 3.2, 2.1875, 3.6571428571, 2.4609375, 4.0634920635, 2.70703125, 4.4329004329, 2.9326171875, 4.7738927739, 3.1420898438, 5.0921522922, 3.338470459, 5.3916906623, 3.52394104, 5.675463855, 3.700138092, 5.9457240386, 3.8683261871, 6.2042337794, more...

decimal, non-monotonic, +

a(n)=n/a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=n%(1+n)/a(n-1)
a(0)=1
n≥0
7 operations
Divisibility
a(n)=n^(2-1)/a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=∑(a(n-1)!)/a(n-1)
a(0)=1
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑(composite(a(n-1)))/a(n-1)
a(0)=1
composite(n)=nth composite number
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence mpt42acs3gazp

1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, 862, 904, 947, 991, 1036, 1082, 1129, 1177, 1226, more...

integer, strictly-monotonic, +, A000124

a(n)=n+a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=1+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=∑(C(n, a(n-1)))
a(0)=1
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=n^(2-1)+a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=n%(1+n)+a(n-1)
a(0)=1
n≥0
7 operations
Divisibility
a(n)=a(n-1)+∑(composite(a(n-1)))
a(0)=1
composite(n)=nth composite number
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence lyijhnkbtmf5p

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

integer, non-monotonic, +-

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

Sequence jhcgnt2oyn0oo

2, 0.5, 4, 0.75, 5.3333333333, 0.9375, 6.4, 1.09375, 7.3142857143, 1.23046875, 8.126984127, 1.353515625, 8.8658008658, 1.4663085938, 9.5477855478, 1.5710449219, 10.1843045843, 1.6692352295, 10.7833813246, 1.76197052, 11.3509277101, 1.850069046, 11.8914480772, 1.9341630936, 12.4084675588, more...

decimal, non-monotonic, +

a(n)=n/a(n-1)
a(0)=2
n≥0
3 operations
Recursive
a(n)=n%(1+n)/a(n-1)
a(0)=2
n≥0
7 operations
Divisibility
a(n)=n^(2-1)/a(n-1)
a(0)=2
n≥0
7 operations
Power
a(n)=n%p(p(n))/a(n-1)
a(0)=2
p(n)=nth prime
n≥0
7 operations
Prime

Sequence xbc4ucyt4ps4m

2, 1, -1, -4, -8, -13, -19, -26, -34, -43, -53, -64, -76, -89, -103, -118, -134, -151, -169, -188, -208, -229, -251, -274, -298, -323, -349, -376, -404, -433, -463, -494, -526, -559, -593, -628, -664, -701, -739, -778, -818, -859, -901, -944, -988, -1033, -1079, -1126, -1174, -1223, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=2
n≥0
3 operations
Recursive
a(n)=2-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=a(n-1)%(2*a(n-1))-n
a(0)=2
n≥0
7 operations
Divisibility

Sequence jg1xfvpx200xk

2, 2, 1, 0.3333333333, 0.0833333333, 0.0166666667, 0.0027777778, 0.0003968254, 0.0000496032, 0.0000055115, 0.0000005511, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

decimal, monotonic, +

a(n)=a(n-1)/n
a(0)=2
n≥0
3 operations
Recursive
a(n)=a(n-1)/n%p(p(n))
a(0)=2
p(n)=nth prime
n≥0
7 operations
Prime

Sequence vthjrkdmos3qp

2, 2, 4, 12, 48, 240, 1440, 10080, 80640, 725760, 7257600, 79833600, 958003200, 12454041600, more...

integer, monotonic, +, A208529

a(n)=n*a(n-1)
a(0)=2
n≥0
3 operations
Recursive
a(n)=2*n!
n≥0
4 operations
Combinatoric
a(n)=n*lcm(a(n-1), 2)
a(0)=2
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=a(n-1)*Ω(∏(a(n-1)))
a(0)=2
∏(a)=partial products of a
Ω(n)=max factorization terms
n≥0
5 operations
Prime

Sequence ul4ltexklmrij

2, 3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173, 192, 212, 233, 255, 278, 302, 327, 353, 380, 408, 437, 467, 498, 530, 563, 597, 632, 668, 705, 743, 782, 822, 863, 905, 948, 992, 1037, 1083, 1130, 1178, 1227, more...

integer, strictly-monotonic, +

a(n)=n+a(n-1)
a(0)=2
n≥0
3 operations
Recursive
a(n)=2+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n%a(n-1)+a(n-1)
a(0)=2
n≥0
5 operations
Divisibility
a(n)=∑(C(n, a(n-1)))
a(0)=2
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=∑(∑(μ(abs(a(n-1)))))
a(0)=2
μ(n)=Möbius function
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence 4h03i2acbvrum

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

integer, non-monotonic, +-

a(n)=n-a(n-1)
a(0)=3
n≥0
3 operations
Recursive

Sequence gfw2uhpgrdtvb

3, 0.3333333333, 6, 0.5, 8, 0.625, 9.6, 0.7291666667, 10.9714285714, 0.8203125, 12.1904761905, 0.90234375, 13.2987012987, 0.9775390625, 14.3216783217, 1.0473632813, 15.2764568765, 1.1128234863, 16.1750719868, 1.1746470133, 17.0263915651, 1.233379364, 17.8371721158, 1.2894420624, 18.6127013382, more...

decimal, non-monotonic, +

a(n)=n/a(n-1)
a(0)=3
n≥0
3 operations
Recursive

Sequence yw1uxhc1cwl5b

3, 2, 0, -3, -7, -12, -18, -25, -33, -42, -52, -63, -75, -88, -102, -117, -133, -150, -168, -187, -207, -228, -250, -273, -297, -322, -348, -375, -403, -432, -462, -493, -525, -558, -592, -627, -663, -700, -738, -777, -817, -858, -900, -943, -987, -1032, -1078, -1125, -1173, -1222, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=3
n≥0
3 operations
Recursive
a(n)=3-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence 5ucked4fci1pp

3, 3, 1.5, 0.5, 0.125, 0.025, 0.0041666667, 0.0005952381, 0.0000744048, 0.0000082672, 0.0000008267, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

decimal, monotonic, +

a(n)=a(n-1)/n
a(0)=3
n≥0
3 operations
Recursive

Sequence yokycpzo01z4e

3, 3, 6, 18, 72, 360, 2160, 15120, 120960, 1088640, 10886400, 119750400, 1437004800, 18681062400, more...

integer, monotonic, +, A052560

a(n)=n*a(n-1)
a(0)=3
n≥0
3 operations
Recursive
a(n)=3*n!
n≥0
4 operations
Combinatoric
a(n)=n*lcm(a(n-1), 3)
a(0)=3
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=Ω(2^n)*a(n-1)
a(0)=3
Ω(n)=max factorization terms
n≥0
6 operations
Prime

Sequence igwhwuompxban

3, 4, 6, 9, 13, 18, 24, 31, 39, 48, 58, 69, 81, 94, 108, 123, 139, 156, 174, 193, 213, 234, 256, 279, 303, 328, 354, 381, 409, 438, 468, 499, 531, 564, 598, 633, 669, 706, 744, 783, 823, 864, 906, 949, 993, 1038, 1084, 1131, 1179, 1228, more...

integer, strictly-monotonic, +, A152950

a(n)=n+a(n-1)
a(0)=3
n≥0
3 operations
Recursive
a(n)=3+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n%a(n-1)+a(n-1)
a(0)=3
n≥0
5 operations
Divisibility
a(n)=∑(C(n, a(n-1)))
a(0)=3
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=(n+a(n-1))%p(a(n-1))
a(0)=3
p(n)=nth prime
n≥0
6 operations
Prime

Sequence pv2vzbuyeyojj

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

integer, non-monotonic, +-

a(n)=n-a(n-1)
a(0)=4
n≥0
3 operations
Recursive

Sequence hcbzrhaxawypg

4, 0.25, 8, 0.375, 10.6666666667, 0.46875, 12.8, 0.546875, 14.6285714286, 0.615234375, 16.253968254, 0.6767578125, 17.7316017316, 0.7331542969, 19.0955710956, 0.7855224609, 20.3686091686, 0.8346176147, 21.5667626491, 0.88098526, 22.7018554201, 0.925034523, 23.7828961544, 0.9670815468, 24.8169351176, more...

decimal, non-monotonic, +

a(n)=n/a(n-1)
a(0)=4
n≥0
3 operations
Recursive

Sequence fydmgbr1xltee

4, 3, 1, -2, -6, -11, -17, -24, -32, -41, -51, -62, -74, -87, -101, -116, -132, -149, -167, -186, -206, -227, -249, -272, -296, -321, -347, -374, -402, -431, -461, -492, -524, -557, -591, -626, -662, -699, -737, -776, -816, -857, -899, -942, -986, -1031, -1077, -1124, -1172, -1221, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=4
n≥0
3 operations
Recursive
a(n)=4-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=(a(n-1)-n)%(n*a(n-1))
a(0)=4
n≥0
7 operations
Divisibility

Sequence dfmvacqrbwxlf

4, 4, 2, 0.6666666667, 0.1666666667, 0.0333333333, 0.0055555556, 0.0007936508, 0.0000992063, 0.0000110229, 0.0000011023, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

decimal, monotonic, +

a(n)=a(n-1)/n
a(0)=4
n≥0
3 operations
Recursive

Sequence iabkx1k1uw4ui

4, 4, 8, 24, 96, 480, 2880, 20160, 161280, 1451520, 14515200, 159667200, 1916006400, 24908083200, more...

integer, monotonic, +

a(n)=n*a(n-1)
a(0)=4
n≥0
3 operations
Recursive
a(n)=4*n!
n≥0
4 operations
Combinatoric
a(n)=n*lcm(a(n-1), 2)
a(0)=4
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility

Sequence rf05oegps3fwd

4, 5, 7, 10, 14, 19, 25, 32, 40, 49, 59, 70, 82, 95, 109, 124, 140, 157, 175, 194, 214, 235, 257, 280, 304, 329, 355, 382, 410, 439, 469, 500, 532, 565, 599, 634, 670, 707, 745, 784, 824, 865, 907, 950, 994, 1039, 1085, 1132, 1180, 1229, more...

integer, strictly-monotonic, +, A145018

a(n)=n+a(n-1)
a(0)=4
n≥0
3 operations
Recursive
a(n)=4+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n%a(n-1)+a(n-1)
a(0)=4
n≥0
5 operations
Divisibility
a(n)=∑(C(n, a(n-1)))
a(0)=4
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=(n+a(n-1))%p(a(n-1))
a(0)=4
p(n)=nth prime
n≥0
6 operations
Prime

Sequence xmhui2mxogfhm

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

integer, non-monotonic, +-

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

Sequence ulpea1ofnsefj

5, 0.2, 10, 0.3, 13.3333333333, 0.375, 16, 0.4375, 18.2857142857, 0.4921875, 20.3174603175, 0.54140625, 22.1645021645, 0.5865234375, 23.8694638695, 0.6284179687, 25.4607614608, 0.6676940918, 26.9584533114, 0.704788208, 28.3773192752, 0.7400276184, 29.728620193, 0.7736652374, 31.0211688971, more...

decimal, non-monotonic, +

a(n)=n/a(n-1)
a(0)=5
n≥0
3 operations
Recursive

Sequence 2trymnzjmmefh

5, 4, 2, -1, -5, -10, -16, -23, -31, -40, -50, -61, -73, -86, -100, -115, -131, -148, -166, -185, -205, -226, -248, -271, -295, -320, -346, -373, -401, -430, -460, -491, -523, -556, -590, -625, -661, -698, -736, -775, -815, -856, -898, -941, -985, -1030, -1076, -1123, -1171, -1220, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=5
n≥0
3 operations
Recursive
a(n)=5-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence ozwhook22m0hi

5, 5, 2.5, 0.8333333333, 0.2083333333, 0.0416666667, 0.0069444444, 0.0009920635, 0.0001240079, 0.0000137787, 0.0000013779, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

decimal, monotonic, +

a(n)=a(n-1)/n
a(0)=5
n≥0
3 operations
Recursive

Sequence owezdnofvqzrh

5, 5, 10, 30, 120, 600, 3600, 25200, 201600, 1814400, 18144000, 199584000, 2395008000, 31135104000, more...

integer, monotonic, +

a(n)=n*a(n-1)
a(0)=5
n≥0
3 operations
Recursive
a(n)=5*n!
n≥0
4 operations
Combinatoric
a(n)=n*lcm(a(n-1), 5)
a(0)=5
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility

Sequence spgub3wpte1il

5, 6, 8, 11, 15, 20, 26, 33, 41, 50, 60, 71, 83, 96, 110, 125, 141, 158, 176, 195, 215, 236, 258, 281, 305, 330, 356, 383, 411, 440, 470, 501, 533, 566, 600, 635, 671, 708, 746, 785, 825, 866, 908, 951, 995, 1040, 1086, 1133, 1181, 1230, more...

integer, strictly-monotonic, +

a(n)=n+a(n-1)
a(0)=5
n≥0
3 operations
Recursive
a(n)=5+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n%a(n-1)+a(n-1)
a(0)=5
n≥0
5 operations
Divisibility
a(n)=∑(C(n, a(n-1)))
a(0)=5
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=(n+a(n-1))%p(a(n-1))
a(0)=5
p(n)=nth prime
n≥0
6 operations
Prime

Sequence 2exstkxj4qg5b

0, 0.8414709848, 0.9092974268, 0.1411200081, -0.7568024953, -0.9589242747, -0.2794154982, 0.6569865987, 0.9893582466, 0.4121184852, -0.5440211109, -0.9999902066, -0.536572918, 0.4201670368, 0.9906073557, 0.6502878402, -0.2879033167, -0.9613974919, -0.7509872468, 0.1498772097, 0.9129452507, 0.8366556385, -0.0088513093, -0.8462204042, -0.905578362, more...

decimal, non-monotonic, +-

a(n)=sin(n)
n≥0
2 operations
Trigonometric
a(n)=sin(∑(a(n-1)!))
a(0)=0
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=sin(∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
4 operations
Prime

Sequence tmed5fpgtxtqj

0, 1.5574077247, -2.1850398633, -0.1425465431, 1.1578212823, -3.3805150062, -0.2910061914, 0.8714479827, -6.7997114552, -0.4523156594, 0.6483608275, -225.9508464542, -0.6358599287, 0.4630211329, 7.2446066161, -0.8559934009, 0.300632242, 3.4939156455, -1.1373137123, 0.1515894706, 2.2371609442, -1.5274985276, 0.008851656, 1.5881530834, -2.1348966977, more...

decimal, non-monotonic, +-

a(n)=tan(n)
n≥0
2 operations
Trigonometric
a(n)=tan(∑(a(n-1)!))
a(0)=0
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=tan(∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
4 operations
Prime

Sequence 1hqdr2ehglqdd

1, 0.5403023059, -0.4161468365, -0.9899924966, -0.6536436209, 0.2836621855, 0.9601702867, 0.7539022543, -0.1455000338, -0.9111302619, -0.8390715291, 0.004425698, 0.8438539587, 0.9074467815, 0.1367372182, -0.7596879129, -0.9576594803, -0.2751633381, 0.6603167082, 0.9887046182, 0.4080820618, -0.5477292602, -0.9999608264, -0.5328330203, 0.4241790073, more...

decimal, non-monotonic, +-

a(n)=cos(n)
n≥0
2 operations
Trigonometric
a(n)=cos(∑(a(n-1)!))
a(0)=0
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=cos(∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
4 operations
Prime

Sequence pzq3co34cjcoc

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

integer, non-monotonic, +

a(n)=stern(stern(n))
stern(n)=Stern-Brocot sequence
n≥0
3 operations
Recursive
a(n)=stern(stern(lcm(n, 2)))
lcm(a,b)=least common multiple
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Divisibility
a(n)=stern(stern(∑(a(n-1)!)))
a(0)=0
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Combinatoric
a(n)=stern(stern(∑(agc(a(n-1)))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Prime

Sequence h3vrmorpscwhg

0, 1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, 819, 1015, 1240, 1496, 1785, 2109, 2470, 2870, 3311, 3795, 4324, 4900, 5525, 6201, 6930, 7714, 8555, 9455, 10416, 11440, 12529, 13685, 14910, 16206, 17575, 19019, 20540, 22140, 23821, 25585, 27434, 29370, 31395, 33511, 35720, 38024, 40425, more...

integer, strictly-monotonic, +, A000330

a(n)=∑(n²)
∑(a)=partial sums of a
n≥0
3 operations
Arithmetic
a(n)=n²+a(n-1)
a(0)=0
n≥0
4 operations
Recursive
a(n)=∑(lcm(n, n²))
lcm(a,b)=least common multiple
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=n^(1+1)+a(n-1)
a(0)=0
n≥0
7 operations
Power
a(n)=∑(∑(a(n-1)!)²)
a(0)=0
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑(∑(agc(a(n-1)))²)
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence ky434qpjxe0ao

0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 64000, 68921, 74088, 79507, 85184, 91125, 97336, 103823, 110592, 117649, more...

integer, strictly-monotonic, +, A000578

a(n)=n^3
n≥0
3 operations
Power
a(n)=n*n²
n≥0
4 operations
Arithmetic
a(n)=∑(a(n-1)!)^3
a(0)=0
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑(agc(a(n-1)))^3
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence rh2c2v1qn0g5g

0, 1, 9, 36, 100, 225, 441, 784, 1296, 2025, 3025, 4356, 6084, 8281, 11025, 14400, 18496, 23409, 29241, 36100, 44100, 53361, 64009, 76176, 90000, 105625, 123201, 142884, 164836, 189225, 216225, 246016, 278784, 314721, 354025, 396900, 443556, 494209, 549081, 608400, 672400, 741321, 815409, 894916, 980100, 1071225, 1168561, 1272384, 1382976, 1500625, more...

integer, strictly-monotonic, +, A000537

a(n)=∑(n)²
∑(a)=partial sums of a
n≥0
3 operations
Arithmetic
a(n)=∑(n^3)
∑(a)=partial sums of a
n≥0
4 operations
Power
a(n)=∑(1+a(n-1))²
a(0)=0
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑(C(n, a(n-1)))²
a(0)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑(∑(agc(a(n-1))))²
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence pj3fnysz04p1i

0, 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000, 14641, 20736, 28561, 38416, 50625, 65536, 83521, 104976, 130321, 160000, 194481, 234256, 279841, 331776, 390625, 456976, 531441, 614656, 707281, 810000, 923521, 1048576, 1185921, 1336336, 1500625, 1679616, 1874161, 2085136, 2313441, 2560000, 2825761, 3111696, 3418801, 3748096, 4100625, 4477456, 4879681, 5308416, 5764801, more...

integer, strictly-monotonic, +, A000583

a(n)=n^4
n≥0
3 operations
Power
a(n)=(n*n)²
n≥0
4 operations
Arithmetic
a(n)=lcm(n, n²)²
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=∑(a(n-1)!)^4
a(0)=0
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑(agc(a(n-1)))^4
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence i41p5reh0akkh

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

integer, non-monotonic, +, A010052

a(n)=cf(n²)
cf(a)=characteristic function of a (in range)
n≥0
3 operations
Arithmetic
a(n)=cf(stern(n)²)
stern(n)=Stern-Brocot sequence
cf(a)=characteristic function of a (in range)
n≥0
4 operations
Recursive
a(n)=cf((n%8)²)
cf(a)=characteristic function of a (in range)
n≥0
5 operations
Divisibility
a(n)=sqrt(cf(n²))
cf(a)=characteristic function of a (in range)
n≥0
4 operations
Power
a(n)=cf(Δ(pt(n))²)
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
cf(a)=characteristic function of a (in range)
n≥0
5 operations
Combinatoric
a(n)=cf(Δ(τ(n))²)
τ(n)=number of divisors of n
Δ(a)=differences of a
cf(a)=characteristic function of a (in range)
n≥1
5 operations
Prime

Sequence 54zyjv03o4o0i

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, more...

integer, strictly-monotonic, +, A005408

a(n)=2+a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=Δ(n²)
Δ(a)=differences of a
n≥0
3 operations
Arithmetic
a(n)=∑(lcm(a(n-1), 2))
a(0)=1
lcm(a,b)=least common multiple
∑(a)=partial sums of a
n≥0
4 operations
Divisibility
a(n)=2^(2-1)+a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=∑(1+pt(a(n-1)))
a(0)=1
pt(n)=Pascals triangle by rows
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑(τ(1+a(n-1)))
a(0)=1
τ(n)=number of divisors of n
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence zdoc3rqfaobde

2, -4, -16, -256, -65536, -4294967296, more...

integer, strictly-monotonic, +-

a(n)=-a(n-1)²
a(0)=2
n≥0
3 operations
Recursive
a(n)=-lcm(a(n-1), 2)²
a(0)=2
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility

Sequence 4ocnuxty54zgg

2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, more...

integer, strictly-monotonic, +, A000037

a(n)=comp(n²)
comp(a)=complement function of a (in range)
n≥0
3 operations
Arithmetic
a(n)=comp(stern(n)²)
stern(n)=Stern-Brocot sequence
comp(a)=complement function of a (in range)
n≥0
4 operations
Recursive
a(n)=comp((n%8)²)
comp(a)=complement function of a (in range)
n≥0
5 operations
Divisibility
a(n)=comp(sqrt(n^4))
comp(a)=complement function of a (in range)
n≥0
5 operations
Power
a(n)=comp(Δ(pt(n))²)
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
comp(a)=complement function of a (in range)
n≥0
5 operations
Combinatoric
a(n)=comp(∑(agc(a(n-1)))²)
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
comp(a)=complement function of a (in range)
n≥0
5 operations
Prime

Sequence gcebkkunvrtdc

3, -9, -81, -6561, -43046721, more...

integer, strictly-monotonic, +-

a(n)=-a(n-1)²
a(0)=3
n≥0
3 operations
Recursive
a(n)=-lcm(a(n-1), 3)²
a(0)=3
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility

Sequence 5zyctci0sedo

4, -16, -256, -65536, -4294967296, more...

integer, strictly-monotonic, +-

a(n)=-a(n-1)²
a(0)=4
n≥0
3 operations
Recursive
a(n)=-lcm(a(n-1), 2)²
a(0)=4
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility

Sequence yxxcoef14wwxe

0, 0, -2, -6, -12, -20, -30, -42, -56, -72, -90, -110, -132, -156, -182, -210, -240, -272, -306, -342, -380, -420, -462, -506, -552, -600, -650, -702, -756, -812, -870, -930, -992, -1056, -1122, -1190, -1260, -1332, -1406, -1482, -1560, -1640, -1722, -1806, -1892, -1980, -2070, -2162, -2256, -2352, more...

integer, monotonic, -

a(n)=n-n²
n≥0
4 operations
Arithmetic
a(n)=(1-n)*2+a(n-1)
a(0)=0
n≥0
7 operations
Recursive
a(n)=n-n^(1+1)
n≥0
7 operations
Power

Sequence fpse24sqf210h

0, 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, more...

integer, monotonic, +, A279019

a(n)=n²-n
n≥0
4 operations
Arithmetic
a(n)=lcm(1-n, n)
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=2*(n-1)+a(n-1)
a(0)=0
n≥0
7 operations
Recursive
a(n)=n^(1+1)-n
n≥0
7 operations
Power

Sequence jxhegbunt3r2p

0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450, more...

integer, strictly-monotonic, +, A002378

a(n)=n+n²
n≥0
4 operations
Arithmetic
a(n)=2*n+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=lcm(1+n, n)
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility
a(n)=n^(1+1)+n
n≥0
7 operations
Power
a(n)=n*∑(a(n-1)!)
a(0)=1
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=n*∑(composite(a(n-1)))
a(0)=1
composite(n)=nth composite number
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence 1r0kz5stvechb

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 20, 15, 6, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 1, 9, 36, 84, 126, more...

integer, non-monotonic, +, A007318

a(n)=pt(n)
pt(n)=Pascals triangle by rows
n≥0
2 operations
Combinatoric
a(n)=pt(∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
pt(n)=Pascals triangle by rows
n≥0
4 operations
Prime

Sequence zu20zaw4iq45h

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134, 105558, 124754, 147273, 173525, more...

integer, monotonic, +, A000041

a(n)=P(n)
P(n)=Partition numbers
n≥0
2 operations
Combinatoric
a(n)=P(∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
P(n)=Partition numbers
n≥0
4 operations
Prime

Sequence itkew3s5ydcwb

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, more...

integer, monotonic, +, A000108

a(n)=catalan(n)
n≥0
2 operations
Combinatoric
a(n)=catalan(∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
4 operations
Prime

Sequence pgkjursh1b3nl

2, 1.4142135624, 1.189207115, 1.0905077327, 1.0442737824, 1.0218971487, 1.0108892861, 1.0054299011, 1.0027112751, 1.0013547199, 1.0006771307, 1.0003385081, 1.0001692397, 1.0000846163, 1.0000423072, 1.0000211534, 1.0000105766, 1.0000052883, 1.0000026442, 1.0000013221, 1.000000661, 1, 1, 1, 1, more...

decimal, strictly-monotonic, +

a(n)=sqrt(a(n-1))
a(0)=2
n≥0
2 operations
Power

Sequence wljobzm1aopbp

3, 1.7320508076, 1.316074013, 1.1472026904, 1.0710754831, 1.0349277671, 1.0173139963, 1.0086198473, 1.0043006757, 1.0021480308, 1.0010734393, 1.0005365757, 1.0002682519, 1.0001341169, 1.0000670562, 1.0000335275, 1.0000167636, 1.0000083818, 1.0000041909, 1.0000020954, 1.0000010477, 1.0000005239, 1, 1, 1, more...

decimal, strictly-monotonic, +

a(n)=sqrt(a(n-1))
a(0)=3
n≥0
2 operations
Power

Sequence 5ftd13eri3ehl

4, 2, 1.4142135624, 1.189207115, 1.0905077327, 1.0442737824, 1.0218971487, 1.0108892861, 1.0054299011, 1.0027112751, 1.0013547199, 1.0006771307, 1.0003385081, 1.0001692397, 1.0000846163, 1.0000423072, 1.0000211534, 1.0000105766, 1.0000052883, 1.0000026442, 1.0000013221, 1.000000661, 1, 1, 1, more...

decimal, strictly-monotonic, +

a(n)=sqrt(a(n-1))
a(0)=4
n≥0
2 operations
Power

Sequence dy55hjjdbdsfl

5, 2.2360679775, 1.4953487812, 1.222844545, 1.105823017, 1.0515811985, 1.0254663322, 1.0126531154, 1.0063066707, 1.0031483792, 1.0015729525, 1.0007861672, 1.0003930064, 1.0001964839, 1.0000982371, 1.0000491174, 1.0000245584, 1.0000122791, 1.0000061395, 1.0000030698, 1.0000015349, 1.0000007674, 1, 1, 1, more...

decimal, strictly-monotonic, +

a(n)=sqrt(a(n-1))
a(0)=5
n≥0
2 operations
Power

Sequence 1echsg1ri0dlc

0, 0, 1, -1, 1, 0, -1, 2, -2, 1, 1, -3, 4, -3, 0, 4, -7, 7, -3, -4, 11, -14, 10, 1, -15, 25, -24, 9, 16, -40, 49, -33, -7, 56, -89, 82, -26, -63, 145, -171, 108, 37, -208, 316, -279, 71, 245, -524, 595, -350, more...

integer, non-monotonic, +-

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

Sequence k2ngedqbfc3km

0, 0, 1, 1, 1, 0, -1, -2, -2, -1, 1, 3, 4, 3, 0, -4, -7, -7, -3, 4, 11, 14, 10, -1, -15, -25, -24, -9, 16, 40, 49, 33, -7, -56, -89, -82, -26, 63, 145, 171, 108, -37, -208, -316, -279, -71, 245, 524, 595, 350, more...

integer, non-monotonic, +-, A050935

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

Sequence fzx54sl1qqlpg

0, 0, 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595, 872, 1278, 1873, 2745, 4023, 5896, 8641, 12664, 18560, 27201, 39865, 58425, 85626, 125491, 183916, 269542, 395033, 578949, 848491, 1243524, 1822473, 2670964, 3914488, 5736961, 8407925, 12322413, 18059374, 26467299, 38789712, more...

integer, monotonic, +

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

Sequence 1zhyi1t2v40zo

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, non-monotonic, +-

a(n)=a(n-2)-a(n-1)
a(0)=0
a(1)=1
n≥0
3 operations
Recursive
a(n)=a(n-2)^(2-1)-a(n-1)
a(0)=0
a(1)=1
n≥0
7 operations
Power
a(n)=a(n-2)%(2*a(n-1))-a(n-1)
a(0)=0
a(1)=1
n≥0
7 operations
Divisibility

Sequence zivzpzr24luqc

0, 1, 1, -1, 2, -1, 0, 2, -3, 3, -1, -2, 5, -6, 4, 1, -7, 11, -10, 3, 8, -18, 21, -13, -5, 26, -39, 34, -8, -31, 65, -73, 42, 23, -96, 138, -115, 19, 119, -234, 253, -134, -100, 353, -487, 387, -34, -453, 840, -874, more...

integer, non-monotonic, +-

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

Sequence kwz2k32shxu1n

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

integer, periodic-6, non-monotonic, +-, A128834

a(n)=a(n-1)-a(n-2)
a(0)=0
a(1)=1
n≥0
3 operations
Recursive
a(n)=a(n-1)%2-a(n-2)
a(0)=0
a(1)=1
n≥0
5 operations
Divisibility
a(n)=a(n-1)^3-a(n-2)
a(0)=0
a(1)=1
n≥0
5 operations
Power

Sequence qcwavvr3jllcl

0, 1, 1, 1, 0, -1, -2, -2, -1, 1, 3, 4, 3, 0, -4, -7, -7, -3, 4, 11, 14, 10, -1, -15, -25, -24, -9, 16, 40, 49, 33, -7, -56, -89, -82, -26, 63, 145, 171, 108, -37, -208, -316, -279, -71, 245, 524, 595, 350, -174, more...

integer, non-monotonic, +-

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

Sequence ki10lzsavzatc

0, 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595, 872, 1278, 1873, 2745, 4023, 5896, 8641, 12664, 18560, 27201, 39865, 58425, 85626, 125491, 183916, 269542, 395033, 578949, 848491, 1243524, 1822473, 2670964, 3914488, 5736961, 8407925, 12322413, 18059374, 26467299, 38789712, 56849086, more...

integer, monotonic, +

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

Sequence 0s52wnlrtxcdm

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)=a(n-1)^(2-1)+a(n-2)
a(0)=0
a(1)=1
n≥0
7 operations
Power
a(n)=a(n-1)%(1+a(n-1))+a(n-2)
a(0)=0
a(1)=1
n≥0
7 operations
Divisibility

Sequence yw3brbn0kgjsc

0, 1, 2, -2, 3, -1, -1, 4, -5, 4, 0, -5, 9, -9, 4, 5, -14, 18, -13, -1, 19, -32, 31, -12, -20, 51, -63, 43, 8, -71, 114, -106, 35, 79, -185, 220, -141, -44, 264, -405, 361, -97, -308, 669, -766, 458, 211, -977, 1435, -1224, more...

integer, non-monotonic, +-

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

Sequence tcwxjdrn0njo

0, 1, 2, 2, 1, -1, -3, -4, -3, 0, 4, 7, 7, 3, -4, -11, -14, -10, 1, 15, 25, 24, 9, -16, -40, -49, -33, 7, 56, 89, 82, 26, -63, -145, -171, -108, 37, 208, 316, 279, 71, -245, -524, -595, -350, 174, 769, 1119, 945, 176, more...

integer, non-monotonic, +-

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

Sequence avvwp50xazwz

0, 1, 2, 2, 3, 4, 8, 3, 4, 12, 11, 6, 10, 19, 18, 4, 5, 24, 34, 11, 18, 24, 13, 14, 18, 39, 28, 20, 31, 46, 32, 5, 6, 40, 69, 36, 46, 33, 62, 20, 29, 66, 42, 37, 24, 38, 53, 22, 26, 89, more...

integer, non-monotonic, +

a(n)=stern(∑(n))
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
3 operations
Recursive
a(n)=stern(lcm(∑(n), 2))
∑(a)=partial sums of a
lcm(a,b)=least common multiple
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Divisibility
a(n)=stern(∑(C(n, a(n-1))))
a(0)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Combinatoric
a(n)=stern(∑(∑(agc(a(n-1)))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Prime

Sequence 5wbnbhw05rv4f

0, 1, 2, 2, 3, 5, 7, 10, 15, 22, 32, 47, 69, 101, 148, 217, 318, 466, 683, 1001, 1467, 2150, 3151, 4618, 6768, 9919, 14537, 21305, 31224, 45761, 67066, 98290, 144051, 211117, 309407, 453458, 664575, 973982, 1427440, 2092015, 3065997, 4493437, 6585452, 9651449, 14144886, 20730338, 30381787, 44526673, 65257011, 95638798, more...

integer, monotonic, +

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

Sequence mrr5xzcftqxsg

0, 1, 2, 4, 5, 8, 10, 13, 14, 18, 21, 26, 28, 33, 36, 40, 41, 46, 50, 57, 60, 68, 73, 80, 82, 89, 94, 102, 105, 112, 116, 121, 122, 128, 133, 142, 146, 157, 164, 174, 177, 188, 196, 209, 214, 226, 233, 242, 244, 253, more...

integer, strictly-monotonic, +, A174868

a(n)=∑(stern(n))
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
3 operations
Recursive
a(n)=∑(stern(lcm(n, 2)))
lcm(a,b)=least common multiple
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑(stern(∑(a(n-1)!)))
a(0)=0
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Combinatoric
a(n)=∑(stern(∑(agc(a(n-1)))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Prime

Sequence zelr4lvgyc1vl

0, 2, -2, 4, -6, 10, -16, 26, -42, 68, -110, 178, -288, 466, -754, 1220, -1974, 3194, -5168, 8362, -13530, 21892, -35422, 57314, -92736, 150050, -242786, 392836, -635622, 1028458, -1664080, 2692538, -4356618, 7049156, -11405774, 18454930, -29860704, 48315634, -78176338, 126491972, -204668310, 331160282, -535828592, 866988874, -1402817466, 2269806340, -3672623806, 5942430146, -9615053952, 15557484098, more...

integer, non-monotonic, +-

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

Sequence pwyanmbd2hpzo

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

integer, periodic-6, non-monotonic, +-

a(n)=a(n-1)-a(n-2)
a(0)=0
a(1)=2
n≥0
3 operations
Recursive
a(n)=a(n-1)%3-a(n-2)
a(0)=0
a(1)=2
n≥0
5 operations
Divisibility

Sequence gmivmeguy2iwb

0, 2, 2, 4, 6, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634, 78176338, 126491972, 204668310, 331160282, 535828592, 866988874, 1402817466, 2269806340, 3672623806, 5942430146, 9615053952, 15557484098, more...

integer, monotonic, +

a(n)=a(n-1)+a(n-2)
a(0)=0
a(1)=2
n≥0
3 operations
Recursive
a(n)=lcm(a(n-1), 2)+a(n-2)
a(0)=0
a(1)=2
lcm(a,b)=least common multiple
n≥0
5 operations
Divisibility

Sequence 21tekj2nlzu5e

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

integer, periodic-6, non-monotonic, +-

a(n)=a(n-1)-a(n-2)
a(0)=1
a(1)=0
n≥0
3 operations
Recursive
a(n)=a(n-1)%2-a(n-2)
a(0)=1
a(1)=0
n≥0
5 operations
Divisibility
a(n)=a(n-1)^3-a(n-2)
a(0)=1
a(1)=0
n≥0
5 operations
Power

Sequence ve5l1ew32nidd

1, 0, 0, -1, -1, -1, 0, 1, 2, 2, 1, -1, -3, -4, -3, 0, 4, 7, 7, 3, -4, -11, -14, -10, 1, 15, 25, 24, 9, -16, -40, -49, -33, 7, 56, 89, 82, 26, -63, -145, -171, -108, 37, 208, 316, 279, 71, -245, -524, -595, more...

integer, non-monotonic, +-, A078013

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

Sequence h1elovzvply0p

1, 0, 0, 1, -1, 1, 0, -1, 2, -2, 1, 1, -3, 4, -3, 0, 4, -7, 7, -3, -4, 11, -14, 10, 1, -15, 25, -24, 9, 16, -40, 49, -33, -7, 56, -89, 82, -26, -63, 145, -171, 108, 37, -208, 316, -279, 71, 245, -524, 595, more...

integer, non-monotonic, +-, A176971

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

Sequence qnuli0qpmf5zb

1, 0, 0, 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 60, 88, 129, 189, 277, 406, 595, 872, 1278, 1873, 2745, 4023, 5896, 8641, 12664, 18560, 27201, 39865, 58425, 85626, 125491, 183916, 269542, 395033, 578949, 848491, 1243524, 1822473, 2670964, 3914488, 5736961, 8407925, 12322413, 18059374, 26467299, more...

integer, non-monotonic, +, A078012

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

Sequence k4nocudelpwdn

1, 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, more...

integer, non-monotonic, +-

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

Sequence cy4jqnfcrgbrf

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

integer, non-monotonic, +-

a(n)=Δ(stern(n))
stern(n)=Stern-Brocot sequence
Δ(a)=differences of a
n≥0
3 operations
Recursive
a(n)=Δ(stern(lcm(n, 2)))
lcm(a,b)=least common multiple
stern(n)=Stern-Brocot sequence
Δ(a)=differences of a
n≥0
5 operations
Divisibility
a(n)=Δ(stern(∑(a(n-1)!)))
a(0)=0
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
Δ(a)=differences of a
n≥0
5 operations
Combinatoric
a(n)=Δ(stern(∑(agc(a(n-1)))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
Δ(a)=differences of a
n≥0
5 operations
Prime

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