Sequence Database

A database with 2076264 machine generated integer and decimal sequences.

Displaying result 0-99 of total 313. [0] [1] [2] [3]

Sequence aq5yo4tvghidg

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

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=de[cosh(cot(68))]
de(a)=decimal expansion of a
n≥0
4 operations
Trigonometric

Sequence kzqkahqfvx5ch

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

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=de[root(25, 18)]
root(n,a)=the n-th root of a
de(a)=decimal expansion of a
n≥0
4 operations
Power

Sequence n3lhf0r02huqe

1, 1, 2, 2, 5, 6, 2, 2, 3, 10, 6, 13, 13, 14, 2, 2, 17, 6, 10, 21, 22, 23, 23, 6, 26, 3, 3, 14, 30, 2, 31, 2, 33, 35, 6, 37, 37, 38, 10, 41, 41, 42, 15, 15, 46, 47, 47, 6, 10, 51, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+Ω(a(n-1)))
a(0)=1
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
n≥0
5 operations
Prime
a(n)=-floor(-rad(n+ω(a(n-1))))
a(0)=1
ω(n)=number of distinct prime divisors of n
rad(n)=square free kernel of n
n≥0
8 operations
Prime

Sequence xevvagfkm0nmk

1, 1, 2, 2, 5, 6, 5, 4, 10, 13, 14, 15, 8, 14, 10, 11, 20, 20, 23, 22, 17, 16, 18, 18, 29, 28, 31, 30, 25, 24, 27, 26, 37, 39, 36, 37, 34, 35, 32, 34, 46, 47, 44, 45, 42, 43, 40, 41, 54, 55, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, ceil(log2(a(n-1))))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
5 operations
Recursive

Sequence bbxisevsoqurb

1, 1, 2, 2, 5, 6, 1, 1, 84, 70, 715, 252, 3432, 10, 27132, 3432, 1540, 3432, 293930, 48620, 80730, 171, 296010, 19, 1037158320, 2704156, 254186856, 1352078, 278256, 40116600, 5586853480, 378, 68923264410, 378, 3773655750150, 2333606220, 67327446062800, 601080390, 53524680, 35345263800, 367290, 15380937, 270533919634160, 15905368710, 45057474, 2104098963720, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=pt(φ(1+n²))
ϕ(n)=number of relative primes (Euler's totient)
pt(n)=Pascals triangle by rows
n≥0
6 operations
Prime

Sequence 1ppjzs2ilyf1n

1, 1, 2, 2, 5, 6, 1, 14, 1, 2, 2, 2, 1, 1, 19, 1, 22, 3, 1, 8, 2, 5, 1, 1, 1, 4, 1, 16, 1, 1, 2, 8, 3, 1, 1, 13, 5, 1, 2, 1, 1, 1, 5, 2, 2, 10, 2, 3, 7, 3, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=contfrac[root(5, 6)-π]
root(n,a)=the n-th root of a
π Pi=3.1415... (Pi)
contfrac(a)=continued fraction of a
n≥0
6 operations
Power

Sequence 2jzaml41o2gxp

1, 1, 2, 2, 5, 6, 2, 2, 3, 11, 6, 13, 14, 15, 2, 2, 17, 19, 10, 10, 21, 22, 6, 5, 5, 26, 14, 29, 31, 31, 2, 2, 33, 35, 6, 37, 38, 39, 10, 10, 41, 43, 15, 15, 46, 46, 47, 7, 10, 10, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+ω(composite(a(n-1))))
a(0)=1
composite(n)=nth composite number
ω(n)=number of distinct prime divisors of n
rad(n)=square free kernel of n
n≥0
6 operations
Prime

Sequence yajqwt3vq5vpp

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

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=Ω(catalan(n)+σ(n))
catalan(n)=the catalan numbers
σ(n)=divisor sum of n
Ω(n)=number of prime divisors of n
n≥1
6 operations
Prime

Sequence voen5cpsykpze

1, 1, 2, 2, 5, 6, 2, 5, 7, 11, 13, 14, 2, 13, 15, 2, 13, 14, 15, 149, 151, 51, 53, 6, 10, 11, 6, 3, 2, 3, 2, 15, 2, 5, 10, 11, 6, 7, 15, 2, 5, 3, 2, 3, 2, 5, 3, 2, 5, 6, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(contfrac[log2(ϕ)]+a(n-1))
a(0)=1
ϕ GoldenRatio=1.618... (Golden Ratio)
contfrac(a)=continued fraction of a
rad(n)=square free kernel of n
n≥0
6 operations
Prime

Sequence j5afb5r3okaql

1, 1, 2, 2, 5, 6, 2, 6, 6, 13, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(xor(n, Ω(catalan(a(n-1)))))
a(0)=1
catalan(n)=the catalan numbers
Ω(n)=number of prime divisors of n
xor(a,b)=bitwise exclusive or
rad(n)=square free kernel of n
n≥0
6 operations
Prime

Sequence 40hjbgsftg0vl

1, 1, 2, 2, 5, 6, 2, 6, 12, 12, 15, 14, 9, 9, 10, 10, 21, 23, 20, 21, 18, 19, 16, 17, 30, 30, 29, 28, 27, 26, 25, 25, 38, 38, 37, 36, 35, 34, 33, 32, 47, 33, 45, 35, 43, 37, 41, 40, 55, 57, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, round(log(a(n-1)²)))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Recursive

Sequence ndg1cowvlad1j

1, 1, 2, 2, 5, 6, 2, 6, 12, 13, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, Ω(catalan(rad(a(n-1)))))
a(0)=1
rad(n)=square free kernel of n
catalan(n)=the catalan numbers
Ω(n)=number of prime divisors of n
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Prime

Sequence lhxlgdysxyhig

1, 1, 2, 2, 5, 6, 2, 6, 12, 14, 2, 10, 10, 11, 8, 10, 22, 27, 30, 30, 25, 30, 27, 27, 20, 19, 19, 18, 21, 23, 21, 21, 42, 49, 48, 49, 54, 54, 53, 52, 59, 61, 63, 62, 57, 57, 58, 59, 36, 62, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, ceil(log2(P(a(n-1)))))
a(0)=1
P(n)=partition numbers
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Combinatoric

Sequence 1qewitrvkeuuc

1, 1, 2, 2, 5, 6, 2, 6, 12, 14, 13, 12, 11, 11, 8, 10, 22, 27, 25, 24, 31, 25, 29, 27, 19, 16, 18, 18, 21, 23, 20, 22, 42, 47, 45, 44, 43, 42, 40, 41, 38, 39, 36, 38, 34, 32, 35, 34, 61, 32, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, ceil(log(a(n-1))²))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Recursive

Sequence ool5rr2z22jof

1, 1, 2, 2, 5, 6, 2, 6, 12, 15, 24, 5, 15, 31, 46, 41, 13, 27, 14, 0, 20, 30, 56, 24, 22, 1, 26, 60, 92, 82, 72, 9, 36, 5, 33, 37, 10, 41, 59, 70, 94, 183, 146, 410, 671, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, stern(C(a(n-1), 2)))
a(0)=1
C(n,k)=binomial coefficient
stern(n)=Stern-Brocot sequence
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Combinatoric

Sequence ebodt1zym2dck

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

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=de[9-(G-π)]
G CatalansConstant=0.9159... (Catalans)
π Pi=3.1415... (Pi)
de(a)=decimal expansion of a
n≥0
6 operations
Arithmetic

Sequence ghgvg1txvikfj

1, 1, 2, 2, 5, 6, 2, 7, 3, 3, 11, 9, 7, 11, 9, 4, 7, 17, 13, 19, 21, 18, 17, 7, 11, 2, 16, 19, 5, 18, 21, 14, 3, 10, 7, 15, 13, 14, 5, 1, 7, 13, 17, 16, 14, 9, 22, 17, 15, 26, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=stern(round(zetazero(n)))%n
zetazero(n)=non trivial zeros of Riemann zeta
stern(n)=Stern-Brocot sequence
n≥2
6 operations
Prime

Sequence yzvjq0letiydc

1, 1, 2, 2, 5, 6, 4, 6, 10, 10, 9, 9, 14, 9, 12, 13, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, ω(gpf(a(n-1))!))
a(0)=1
gpf(n)=greatest prime factor of n
ω(n)=number of distinct prime divisors of n
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Prime

Sequence omd1nr3dmjk1b

1, 1, 2, 2, 5, 6, 4, 6, 10, 10, 9, 9, 14, 14, 13, 11, 20, 18, 16, 18, 22, 17, 19, 18, 26, 29, 31, 30, 31, 24, 28, 28, 35, 34, 39, 39, 32, 36, 36, 37, 46, 44, 46, 46, 41, 43, 40, 44, 52, 53, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, ceil(log2(gpf(a(n-1)))))
a(0)=1
gpf(n)=greatest prime factor of n
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Prime

Sequence hae2pii4snokh

1, 1, 2, 2, 5, 6, 4, 6, 10, 10, 9, 15, 8, 12, 12, 13, 21, 25, 21, 27, 28, 22, 19, 16, 25, 30, 30, 31, 25, 26, 27, 23, 39, 43, 47, 42, 44, 32, 39, 45, 36, 45, 38, 44, 41, 38, 41, 36, 52, 52, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, stern(a(n-1))%a(n-1))
a(0)=1
stern(n)=Stern-Brocot sequence
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Recursive

Sequence gx0fy1xp5t1y

1, 1, 2, 2, 5, 6, 5, 2, 3, 11, 14, 15, 2, 6, 13, 11, 10, 21, 23, 22, 17, 2, 23, 6, 3, 3, 6, 6, 31, 6, 29, 26, 37, 39, 6, 2, 37, 35, 2, 38, 46, 47, 22, 46, 42, 43, 10, 43, 6, 10, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(xor(n, ceil(log2(a(n-1)))))
a(0)=1
xor(a,b)=bitwise exclusive or
rad(n)=square free kernel of n
n≥0
6 operations
Prime

Sequence p5ecwqvpykdzj

1, 1, 2, 2, 5, 6, 5, 4, 9, 8, 11, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, ω(catalan(rad(a(n-1)))))
a(0)=1
rad(n)=square free kernel of n
catalan(n)=the catalan numbers
ω(n)=number of distinct prime divisors of n
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Prime

Sequence jnm1b524cklzo

1, 1, 2, 2, 5, 6, 5, 4, 9, 11, 14, 15, 8, 12, 13, 11, 20, 21, 23, 22, 17, 16, 23, 18, 27, 27, 24, 24, 31, 24, 29, 26, 37, 39, 36, 32, 37, 35, 32, 38, 46, 47, 44, 46, 42, 43, 40, 43, 54, 50, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, ceil(log2(rad(a(n-1)))))
a(0)=1
rad(n)=square free kernel of n
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Prime

Sequence onvcdlgv3dftn

1, 1, 2, 2, 5, 6, 5, 4, 10, 10, 9, 9, 14, 14, 13, 12, 19, 18, 22, 16, 23, 22, 21, 20, 27, 29, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, ω(P(composite(a(n-1)))))
a(0)=1
composite(n)=nth composite number
P(n)=partition numbers
ω(n)=number of distinct prime divisors of n
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Prime

Sequence q44n5mv033qyo

1, 1, 2, 2, 5, 6, 5, 4, 10, 10, 9, 14, 15, 8, 10, 12, 19, 21, 22, 22, 17, 16, 21, 19, 28, 28, 31, 24, 24, 25, 31, 28, 37, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, Ω(P(composite(a(n-1)))))
a(0)=1
composite(n)=nth composite number
P(n)=partition numbers
Ω(n)=number of prime divisors of n
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Prime

Sequence p0idgka124dce

1, 1, 2, 2, 5, 6, 5, 4, 10, 12, 12, 13, 11, 11, 8, 11, 22, 27, 30, 31, 25, 30, 26, 28, 20, 16, 18, 18, 21, 23, 20, 22, 42, 49, 51, 49, 53, 55, 53, 53, 58, 58, 57, 56, 63, 56, 61, 59, 36, 63, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, round(log2(P(a(n-1)))))
a(0)=1
P(n)=partition numbers
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Combinatoric

Sequence 4irbte5eu4iwi

1, 1, 2, 2, 5, 6, 5, 4, 10, 13, 15, 14, 9, 9, 10, 11, 20, 20, 23, 21, 18, 16, 19, 18, 29, 31, 28, 29, 26, 27, 24, 25, 38, 38, 37, 36, 35, 34, 33, 33, 46, 46, 45, 44, 43, 42, 41, 40, 55, 57, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, floor(log(a(n-1)²)))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Recursive

Sequence 2rdfajndjbdxj

1, 1, 2, 2, 5, 6, 5, 4, 10, 15, 3, 10, 10, 11, 8, 11, 22, 28, 3, 18, 31, 6, 21, 27, 8, 29, 11, 29, 13, 21, 18, 20, 44, 58, 1, 35, 49, 59, 2, 38, 63, 15, 35, 62, 10, 43, 52, 15, 57, 18, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, floor(a(n-1)/ϕ))
a(0)=1
ϕ GoldenRatio=1.618... (Golden Ratio)
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Recursive

Sequence hgytibo0ucgrj

1, 1, 2, 2, 5, 6, 5, 4, 10, 15, 14, 13, 15, 9, 11, 10, 22, 25, 26, 26, 29, 28, 16, 31, 17, 30, 18, 19, 25, 21, 24, 26, 41, 43, 40, 47, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, Ω(σ(P(a(n-1)))))
a(0)=1
P(n)=partition numbers
σ(n)=divisor sum of n
Ω(n)=number of prime divisors of n
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Prime

Sequence u3kibydkhl5xm

1, 1, 2, 2, 5, 6, 5, 4, 11, 10, 14, 15, 9, 9, 10, 11, 19, 21, 23, 16, 19, 17, 19, 19, 28, 31, 30, 29, 24, 26, 27, 25, 37, 36, 37, 38, 33, 32, 47, 36, 47, 42, 44, 45, 43, 41, 43, 43, 52, 54, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, Ω(φ(a(n-1)²)))
a(0)=1
ϕ(n)=number of relative primes (Euler's totient)
Ω(n)=number of prime divisors of n
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Prime

Sequence 3oyssterchtjd

1, 1, 2, 2, 5, 6, 5, 6, 7, 7, 7, 5, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=and(7, P(τ(catalan(n))))
catalan(n)=the catalan numbers
τ(n)=number of divisors of n
P(n)=partition numbers
and(a,b)=bitwise and
n≥0
6 operations
Prime
a(n)=P(τ(catalan(n)))%8
catalan(n)=the catalan numbers
τ(n)=number of divisors of n
P(n)=partition numbers
n≥0
6 operations
Prime

Sequence iinh4tm4y4w3e

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

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+ω(a(n-1)))%9
a(0)=1
ω(n)=number of distinct prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence 4xmpaylu4r3dk

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

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+Ω(a(n-1)))%9
a(0)=1
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence 0x4ipln2nrhle

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

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+ω(a(n-1)))%8
a(0)=1
ω(n)=number of distinct prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime
a(n)=rad(n+Ω(a(n-1)))%8
a(0)=1
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence 5ozs1ladgklmn

1, 1, 2, 2, 5, 6, 2, 2, 3, 10, 6, 1, 6, 3, 3, 2, 5, 6, 10, 9, 9, 10, 6, 5, 5, 2, 3, 2, 5, 6, 2, 2, 9, 10, 6, 1, 6, 3, 3, 10, 6, 7, 7, 10, 10, 11, 11, 6, 10, 3, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+ω(a(n-1)))%12
a(0)=1
ω(n)=number of distinct prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence equk3yjauor1c

1, 1, 2, 2, 5, 6, 2, 2, 3, 10, 6, 1, 6, 3, 3, 2, 5, 6, 10, 9, 10, 11, 11, 6, 2, 2, 3, 2, 5, 6, 2, 2, 9, 11, 11, 6, 2, 2, 3, 10, 6, 7, 7, 10, 10, 11, 11, 6, 10, 3, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+Ω(a(n-1)))%12
a(0)=1
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence i3offs5xli2wn

1, 1, 2, 2, 5, 6, 2, 2, 3, 10, 6, 2, 2, 3, 2, 5, 6, 2, 2, 3, 10, 6, 2, 2, 3, 2, 5, 6, 2, 2, 3, 10, 6, 2, 2, 3, 2, 5, 6, 2, 2, 3, 10, 6, 2, 2, 3, 2, 5, 6, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n%11+Ω(a(n-1)))
a(0)=1
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence 0xxy1kvelwxom

1, 1, 2, 2, 5, 6, 2, 2, 3, 10, 6, 6, 14, 14, 2, 15, 17, 6, 10, 10, 22, 23, 6, 6, 26, 26, 14, 14, 30, 30, 33, 2, 33, 35, 6, 37, 38, 38, 10, 41, 42, 42, 15, 22, 46, 47, 6, 6, 10, 10, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+ω(n)%a(n-1))
a(0)=1
ω(n)=number of distinct prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence adf1of4jxpnvm

1, 1, 2, 2, 5, 6, 2, 2, 3, 10, 6, 13, 13, 14, 2, 2, 3, 2, 5, 6, 2, 2, 3, 10, 6, 13, 13, 14, 2, 2, 3, 2, 5, 6, 2, 2, 3, 10, 6, 13, 13, 14, 2, 2, 3, 2, 5, 6, 2, 2, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n%14+Ω(a(n-1)))
a(0)=1
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence wy21iftjvzejc

1, 1, 2, 2, 5, 6, 2, 2, 3, 10, 6, 13, 13, 14, 2, 2, 17, 6, 10, 21, 22, 23, 23, 6, 26, 3, 3, 14, 30, 29, 31, 2, 33, 35, 6, 37, 37, 38, 10, 41, 41, 42, 42, 43, 15, 47, 47, 6, 10, 51, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+Ω(a(n-1))%3)
a(0)=1
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence oyvssa3lrh1ge

1, 1, 2, 2, 5, 6, 2, 2, 3, 10, 6, 13, 13, 14, 15, 2, 17, 19, 10, 21, 22, 22, 23, 6, 26, 26, 3, 14, 29, 30, 2, 2, 33, 35, 6, 37, 37, 38, 10, 41, 41, 42, 22, 22, 15, 46, 6, 7, 7, 10, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+ω(τ(σ(a(n-1)))))
a(0)=1
σ(n)=divisor sum of n
τ(n)=number of divisors of n
ω(n)=number of distinct prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence bjnqbwoejmsjn

1, 1, 2, 2, 5, 6, 2, 2, 3, 10, 6, 13, 14, 2, 15, 6, 6, 19, 21, 23, 23, 6, 6, 5, 5, 26, 29, 30, 2, 30, 34, 34, 35, 37, 37, 38, 10, 39, 42, 22, 43, 22, 15, 46, 6, 47, 10, 7, 10, 51, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+Ω(φ(σ(a(n-1)))))
a(0)=1
σ(n)=divisor sum of n
ϕ(n)=number of relative primes (Euler's totient)
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence hyzamafb3l0id

1, 1, 2, 2, 5, 6, 2, 2, 3, 10, 6, 13, 14, 2, 15, 17, 17, 6, 10, 21, 23, 23, 6, 5, 5, 26, 29, 29, 30, 2, 31, 33, 35, 6, 6, 37, 39, 10, 10, 41, 41, 42, 46, 15, 46, 47, 6, 7, 10, 51, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+ω(σ(a(n-1)²)))
a(0)=1
σ(n)=divisor sum of n
ω(n)=number of distinct prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence 5vardhzyescmc

1, 1, 2, 2, 5, 6, 2, 2, 3, 10, 6, 13, 14, 2, 15, 17, 17, 6, 10, 21, 23, 23, 6, 5, 5, 26, 29, 29, 30, 2, 31, 33, 35, 6, 6, 37, 39, 10, 10, 41, 41, 42, 46, 46, 47, 47, 6, 7, 10, 51, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+Ω(σ(a(n-1)²)))
a(0)=1
σ(n)=divisor sum of n
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence lpmmppixkdyrm

1, 1, 2, 2, 5, 6, 2, 2, 3, 10, 13, 14, 2, 14, 6, 17, 10, 10, 21, 6, 22, 3, 23, 29, 31, 33, 34, 6, 30, 37, 39, 41, 42, 22, 10, 38, 46, 7, 10, 42, 51, 6, 22, 7, 46, 57, 30, 55, 62, 65, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(round(n+a(n-1)/4))
a(0)=1
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence khudwkylsql0e

1, 1, 2, 2, 5, 6, 2, 4, 4, 6, 3, 6, 16, 4, 8, 2, 16, 4, 12, 12, 6, 8, 16, 24, 18, 8, 8, 8, 4, 2, 4, 4, 8, 6, 4, 16, 8, 8, 2, 4, 2, 4, 10, 2, 12, 56, 4, 8, 24, 10, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=τ(∑[n²]+τ(a(n-1)))
a(0)=1
∑(a)=partial sums of a
τ(n)=number of divisors of n
n≥0
7 operations
Prime

Sequence s5yefz5orzxhj

1, 1, 2, 2, 5, 6, 2, 5, 6, 15, 6, 15, 6, 2, 6, 6, 21, 6, 10, 6, 10, 2, 2, 6, 30, 30, 30, 30, 30, 6, 2, 7, 6, 21, 6, 10, 15, 30, 6, 21, 6, 10, 6, 30, 6, 6, 6, 21, 2, 10, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(τ(a(n-1)²*φ(n)))
a(0)=1
ϕ(n)=number of relative primes (Euler's totient)
τ(n)=number of divisors of n
rad(n)=square free kernel of n
n≥1
7 operations
Prime

Sequence aacmqv2j5kjak

1, 1, 2, 2, 5, 6, 2, 6, 12, 0, 10, 12, 5, 14, 4, 13, 25, 5, 17, 30, 13, 28, 1, 23, 10, 30, 3, 26, 9, 27, 8, 26, 53, 15, 41, 0, 36, 59, 21, 55, 24, 58, 24, 56, 29, 53, 0, 47, 24, 34, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, round(a(n-1)-sqrt(a(n-1))))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Recursive

Sequence rnmndyvkoceni

1, 1, 2, 2, 5, 6, 2, 6, 12, 0, 10, 12, 5, 14, 5, 12, 25, 5, 17, 30, 13, 31, 12, 30, 1, 25, 14, 16, 16, 17, 19, 16, 44, 7, 39, 2, 37, 58, 21, 54, 7, 44, 12, 34, 49, 7, 43, 10, 55, 1, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, ceil(a(n-1)-sqrt(a(n-1))))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Recursive

Sequence tj5ldqwbuvrdl

1, 1, 2, 2, 5, 6, 2, 6, 12, 1, 10, 12, 4, 15, 4, 13, 25, 0, 18, 31, 1, 21, 24, 7, 28, 10, 29, 15, 22, 18, 18, 19, 45, 62, 9, 37, 62, 14, 47, 6, 44, 54, 12, 35, 52, 9, 40, 51, 20, 63, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, floor(a(n-1)/sqrt(2)))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Recursive

Sequence lucrfvdagibfe

1, 1, 2, 2, 5, 6, 2, 6, 12, 1, 10, 12, 4, 15, 4, 13, 25, 0, 18, 31, 2, 20, 24, 6, 28, 10, 29, 15, 22, 18, 18, 19, 45, 62, 9, 37, 62, 14, 44, 56, 15, 35, 50, 8, 41, 48, 12, 39, 43, 47, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, round(sqrt(C(a(n-1), 2))))
a(0)=1
C(n,k)=binomial coefficient
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Combinatoric

Sequence 1m2ug2b10aysb

1, 1, 2, 2, 5, 6, 2, 6, 12, 1, 10, 12, 4, 15, 4, 13, 25, 3, 16, 24, 5, 22, 25, 5, 27, 10, 29, 15, 22, 18, 18, 19, 45, 1, 34, 59, 14, 47, 7, 34, 48, 11, 45, 11, 43, 50, 10, 40, 44, 46, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, floor(a(n-1)/log(4)))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Recursive

Sequence sssvaa0nwhsxg

1, 1, 2, 2, 5, 6, 2, 6, 12, 1, 10, 13, 5, 14, 7, 11, 23, 30, 6, 23, 27, 7, 18, 27, 10, 31, 15, 17, 23, 18, 18, 19, 45, 62, 8, 38, 62, 15, 44, 57, 15, 35, 50, 9, 42, 48, 15, 37, 41, 45, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, floor(log(2)*a(n-1)))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Recursive

Sequence etkda2lts1eyj

1, 1, 2, 2, 5, 6, 2, 7, 9, -2, -26, -33, -101, -538, -2264, -3993, -5705, -14362, -100748, -964761, -5284749, -9604762, -13924752, -39844761, -428644737, -8204644762, -124844644740, -824684644761, -1524524644741, -2224364644762, -7123244644744, -109999724644761, -3710676524644793, more...

integer, non-monotonic, +-, A000403 (weak, multiple)

a(n)=xor(n, a(n-1)-∏[pt(n)])
a(0)=1
pt(n)=Pascals triangle by rows
∏(a)=partial products of a
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Combinatoric

Sequence jjjw2sytredkk

1, 1, 2, 2, 5, 6, 3, 2, 3, 10, 13, 6, 15, 2, 15, 6, 19, 6, 21, 22, 23, 22, 5, 6, 3, 26, 29, 14, 31, 30, 37, 2, 33, 6, 37, 6, 39, 10, 41, 10, 43, 42, 7, 22, 47, 46, 7, 6, 51, 26, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n-1+τ(a(n-1)))
a(0)=1
τ(n)=number of divisors of n
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence cmdexfhqf4cmi

1, 1, 2, 2, 5, 6, 3, 3, 11, 14, 4, 2, 5, 21, 23, 4, 2, 2, 6, 35, 36, 6, 1, 1, 2, 7, 51, 53, 6, 1, 0, 0, 1, 8, 74, 75, 8, 1, 0, 0, 0, 1, 10, 96, 98, 8, 1, 0, 0, 0, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=floor(p(n)/p(pt(n)))
p(n)=nth prime
pt(n)=Pascals triangle by rows
n≥1
7 operations
Prime

Sequence ospujc1wpn1gd

1, 1, 2, 2, 5, 6, 3, 6, 9, 11, 3, 10, 13, 5, 10, 6, 17, 1, 18, 2, 21, 16, 31, 24, 29, 31, 18, 30, 11, 24, 31, 20, 51, 50, 57, 34, 57, 46, 51, 37, 44, 44, 45, 32, 41, 57, 52, 46, 25, 61, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, p(composite(n))%a(n-1))
a(0)=1
composite(n)=nth composite number
p(n)=nth prime
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Prime

Sequence 0ev354z5c2vhk

1, 1, 2, 2, 5, 6, 3, 6, 12, 3, 11, 12, 6, 15, 3, -16, -4, -27, -15, -8, -32, -55, -45, -34, -62, -93, -123, -156, -132, -147, -137, -144, -184, -159, -133, -176, -152, -135, -171, -150, -182, -237, -219, -206, -250, -301, -281, -258, -314, -373, more...

integer, non-monotonic, +-, A000403 (weak, multiple)

a(n)=xor(n, a(n-1)-φ(φ(n)))
a(0)=1
ϕ(n)=number of relative primes (Euler's totient)
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Prime

Sequence ydwx3lipcayif

1, 1, 2, 2, 5, 6, 3, 6, 13, 1, 10, 8, 15, 3, 15, 1, 16, 16, 19, 31, 31, 30, 27, 18, 21, 28, 31, 16, 29, 26, 25, 30, 45, 4, 33, 58, 39, 50, 9, 37, 57, 30, 39, 60, 45, 8, 45, 10, 51, 26, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, p(composite(a(n-1)))%a(n-1))
a(0)=1
composite(n)=nth composite number
p(n)=nth prime
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Prime

Sequence 1w4xycgcy4vnh

1, 1, 2, 2, 5, 6, 3, 6, 13, 59, 415916, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, floor(P(a(n-1))/2))
a(0)=1
P(n)=partition numbers
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Combinatoric

Sequence sfl4blwwgvw3p

1, 1, 2, 2, 5, 6, 3, 7, 7, 15, 9, 5, 11, 23, 33, 14, 15, 12, 13, 27, 3, 7, 15, 6, 15, 29, 33, 32, 9, 16, 3, 7, 15, 29, 59, 84, 15, 29, 59, 80, 31, 63, 27, 43, 43, 87, 57, 52, 15, 29, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=σ(a(n-1))%n+gpf(a(n-1))
a(0)=1
σ(n)=divisor sum of n
gpf(n)=greatest prime factor of n
n≥0
7 operations
Prime
a(n)=gpf(a(n-1))--σ(a(n-1))%n
a(0)=1
gpf(n)=greatest prime factor of n
σ(n)=divisor sum of n
n≥0
8 operations
Prime

Sequence ikiai1rfy3cge

1, 1, 2, 2, 5, 6, 4, 0, 3, 8, -14, -728, -748, -747, -744, -858, -3629652, -7258450, -7258564, -7258561, -7258560, -7259274, -1307681627270, more...

integer, non-monotonic, +-, A000403 (weak, multiple)

a(n)=p(n)-∑[pt(n)!]
p(n)=nth prime
pt(n)=Pascals triangle by rows
∑(a)=partial sums of a
n≥1
7 operations
Prime

Sequence yznuojawnxqp

1, 1, 2, 2, 5, 6, 4, 4, 9, 10, 6, 6, 13, 14, 8, 16, 17, 18, 19, 10, 11, 22, 23, 24, 25, 13, 27, 28, 15, 15, 31, 32, 17, 34, 35, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=ceil(n/Δ[comp[p(n)]])
p(n)=nth prime
comp(a)=complement function of a (in range)
Δ(a)=differences of a
n≥1
7 operations
Prime

Sequence zigbw54qope2j

1, 1, 2, 2, 5, 6, 4, 6, 8, 10, 9, 12, 9, 13, 15, 15, 17, 16, 18, 18, 20, 21, 23, 22, 23, 25, 27, 26, 29, 27, 30, 29, 32, 33, 35, 34, 35, 36, 39, 39, 40, 40, 42, 42, 39, 44, 46, 45, 46, 49, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=n-Ω(∑[τ(τ(n))])
τ(n)=number of divisors of n
∑(a)=partial sums of a
Ω(n)=number of prime divisors of n
n≥2
7 operations
Prime

Sequence pf1yzpbupzuxl

1, 1, 2, 2, 5, 6, 5, 2, 3, 10, 3, 6, 11, 14, 13, 2, 17, 6, 17, 10, 19, 22, 21, 22, 23, 26, 5, 14, 3, 30, 31, 2, 33, 2, 35, 34, 35, 6, 37, 10, 39, 10, 41, 22, 43, 46, 15, 46, 47, 10, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n-λ(a(n-1))%a(n-1))
a(0)=1
λ(n)=Liouville's function
rad(n)=square free kernel of n
n≥0
7 operations
Prime

Sequence tv3cz3empj0ro

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

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, ω(a(n-1)!))%7
a(0)=1
ω(n)=number of distinct prime divisors of n
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Prime

Sequence r3spoy4sw0ikk

1, 1, 2, 2, 5, 6, 5, 4, 9, 10, 12, 13, 10, 11, 8, 12, 22, 27, 29, 28, 27, 26, 25, 29, 23, 19, 16, 29, 19, 23, 20, 21, 42, 52, 62, 63, 56, 57, 58, 59, 52, 53, 54, 55, 48, 56, 50, 51, 44, 36, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, C(ceil(sqrt(a(n-1))), 2))
a(0)=1
C(n,k)=binomial coefficient
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Combinatoric

Sequence 0rhjm4ach0l0g

1, 1, 2, 2, 5, 6, 5, 4, 9, 12, 9, 14, 5, 14, 7, 12, 19, 18, 29, 16, 29, 22, 31, 20, 23, 26, 19, 24, 9, 24, 11, 28, 47, 34, 43, 32, 47, 38, 47, 36, 49, 44, 37, 40, 57, 36, 55, 38, 57, 56, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, τ(a(n-1)²)%a(n-1))
a(0)=1
τ(n)=number of divisors of n
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Prime

Sequence brmyuiqzdjrqb

1, 1, 2, 2, 5, 6, 5, 4, 10, 8, 10, 10, 13, 14, 13, 12, 18, 16, 18, 18, 21, 22, 21, 20, 26, 24, 26, 26, 29, 30, 29, 28, 34, 32, 34, 34, 37, 38, 37, 36, 42, 40, 42, 42, 45, 46, 45, 44, 50, 48, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, ω(and(7, a(n-1))!))
a(0)=1
and(a,b)=bitwise and
ω(n)=number of distinct prime divisors of n
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Prime

Sequence 1yijmowhcftpg

1, 1, 2, 2, 5, 6, 5, 4, 10, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 18, 21, 20, 23, 22, 25, 24, 27, 26, 29, 28, 31, 30, 33, 35, 32, 34, 38, 39, 36, 37, 42, 43, 40, 41, 46, 47, 44, 45, 50, 51, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, and(3, ceil(log2(a(n-1)))))
a(0)=1
and(a,b)=bitwise and
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Recursive

Sequence vyhgtukmdxbrp

1, 1, 2, 2, 5, 6, 5, 4, 10, 11, 8, 11, 14, 13, 13, 12, 19, 18, 16, 18, 22, 21, 22, 23, 25, 27, 25, 25, 30, 28, 30, 30, 33, 34, 33, 32, 38, 39, 36, 39, 42, 41, 41, 40, 47, 46, 44, 46, 50, 49, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, ω((a(n-1)%7)!))
a(0)=1
ω(n)=number of distinct prime divisors of n
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Prime

Sequence dtxxrzlpnhheb

1, 1, 2, 2, 5, 6, 5, 4, 10, 12, 12, 13, 11, 11, 8, 11, 22, 26, 30, 29, 26, 25, 26, 27, 21, 19, 19, 18, 21, 23, 21, 21, 42, 50, 53, 59, 63, 57, 60, 60, 51, 62, 54, 50, 59, 54, 55, 54, 41, 34, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, floor(composite(a(n-1))/3))
a(0)=1
composite(n)=nth composite number
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Prime

Sequence zw0uf003u4bch

1, 1, 2, 2, 5, 6, 5, 4, 10, 15, 0, 11, 11, 10, 8, 10, 22, 30, 6, 16, 30, 1, 22, 24, 8, 28, 9, 29, 8, 24, 14, 22, 47, 1, 34, 52, 0, 37, 63, 11, 47, 9, 44, 53, 9, 43, 48, 14, 57, 22, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, floor(sqrt(C(a(n-1), 2))))
a(0)=1
C(n,k)=binomial coefficient
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Combinatoric

Sequence oauntzxqoh2bn

1, 1, 2, 2, 5, 6, 5, 4, 10, 15, 3, 10, 10, 11, 8, 10, 22, 28, 3, 18, 31, 6, 21, 26, 8, 28, 11, 29, 14, 21, 19, 20, 44, 58, 6, 32, 48, 59, 3, 38, 63, 14, 34, 62, 11, 43, 53, 14, 56, 18, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, floor(a(n-1)/log2(3)))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Recursive

Sequence mfgwm0fhyohpf

1, 1, 2, 2, 5, 6, 5, 4, 10, 15, 3, 10, 10, 11, 8, 11, 22, 28, 3, 18, 31, 6, 21, 26, 8, 29, 8, 31, 15, 20, 18, 20, 44, 58, 6, 32, 55, 7, 34, 50, 55, 11, 44, 48, 49, 51, 49, 49, 46, 45, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, floor(a(n-1)/log(5)))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Recursive

Sequence o5mimr5rjmkoo

1, 1, 2, 2, 5, 6, 5, 4, 11, 10, 9, 8, 15, 14, 13, 12, 19, 18, 17, 16, 23, 22, 21, 20, 27, 26, 25, 24, 31, 30, 29, 28, 35, 34, 33, 32, 39, 38, 37, 36, 43, 42, 41, 40, 47, 46, 45, 44, 51, 50, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, (3+a(n-1))%a(n-1))
a(0)=1
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Recursive

Sequence wn35u4zc5b2vh

1, 1, 2, 2, 5, 6, 5, 4, 11, 12, 3, 11, 8, 14, 7, 13, 25, 18, 29, 16, 27, 28, 31, 20, 25, 28, 19, 28, 19, 30, 5, 28, 43, 40, 43, 42, 61, 38, 47, 46, 61, 42, 49, 40, 35, 34, 39, 44, 43, 52, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, τ(n²)%a(n-1))
a(0)=1
τ(n)=number of divisors of n
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Prime

Sequence skd2l12uqcsem

1, 1, 2, 2, 5, 6, 5, 4, 11, 15, 2, 10, 9, 8, 11, 9, 21, 26, 31, 28, 25, 25, 26, 26, 21, 18, 19, 18, 21, 22, 21, 20, 42, 50, 53, 58, 63, 56, 60, 60, 51, 62, 54, 50, 59, 54, 55, 54, 41, 34, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, round(composite(a(n-1))/3))
a(0)=1
composite(n)=nth composite number
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Prime

Sequence cav5b51pvx2kp

1, 1, 2, 2, 5, 6, 5, 6, 8, 12, 8, 11, 10, 5, 10, 15, 23, 17, 21, 23, 23, 17, 26, 19, 20, 21, 22, 23, 16, 24, 16, 24, 48, 8, 32, 40, 32, 43, 34, 41, 32, 59, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=xor(n, comp[∑[n]]%a(n-1))
a(0)=1
∑(a)=partial sums of a
comp(a)=complement function of a (in range)
xor(a,b)=bitwise exclusive or
n≥0
7 operations
Recursive

Sequence xtkqj1shq5lsp

1, 1, 2, 2, 5, 6, 5, 6, 10, 9, 5, 6, 10, 6, 5, 9, 17, 2, 10, 6, 10, 9, 5, 6, 17, 5, 9, 10, 14, 2, 10, 6, 26, 5, 9, 5, 21, 2, 5, 9, 17, 2, 10, 6, 10, 14, 5, 6, 26, 5, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=gcd(a(n-1), 5)+Ω(n)²
a(0)=1
gcd(a,b)=greatest common divisor
Ω(n)=number of prime divisors of n
n≥0
7 operations
Prime
a(n)=gcd(rad(a(n-1)), 5)+Ω(n)²
a(0)=1
rad(n)=square free kernel of n
gcd(a,b)=greatest common divisor
Ω(n)=number of prime divisors of n
n≥0
8 operations
Prime
a(n)=gcd(gpf(a(n-1)), 5)+Ω(n)²
a(0)=1
gpf(n)=greatest prime factor of n
gcd(a,b)=greatest common divisor
Ω(n)=number of prime divisors of n
n≥0
8 operations
Prime

Sequence ofghlztwauvxm

1, 1, 2, 2, 5, 6, 5, 7, 9, 10, 10, 10, 11, 13, 15, 15, 15, 16, 18, 18, 21, 22, 23, 23, 23, 25, 26, 26, 29, 30, 31, 31, 31, 34, 34, 36, 35, 37, 37, 39, 40, 40, 42, 44, 43, 44, 47, 47, 49, 49, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=n-μ(∑[xor(5, n)])
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
μ(n)=Möbius function
n≥0
7 operations
Prime

Sequence dil5cptvxknvd

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

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=(n^Ω(6+n))%7
Ω(n)=number of prime divisors of n
n≥1
8 operations
Prime

Sequence zeybqnn14tgpk

1, 1, 2, 2, 5, 6, 0, 2, 7, 6, 6, 11, 11, 13, 8, 5, 1, 8, 10, 16, 9, 11, 20, 11, 23, 17, 26, 10, 21, 18, 24, 16, 15, 20, 34, 11, 37, 37, 28, 34, 19, 4, 22, 28, 15, 14, 32, 48, 31, 33, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=∑[∑[∑[φ(n)²]]]%n
ϕ(n)=number of relative primes (Euler's totient)
∑(a)=partial sums of a
n≥2
8 operations
Prime

Sequence wswotz02uohve

1, 1, 2, 2, 5, 6, 1, 2, 7, 2, 5, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=Ω(lcm(n^(a(n-1)%6), 3))
a(0)=1
lcm(a,b)=least common multiple
Ω(n)=number of prime divisors of n
n≥0
8 operations
Prime

Sequence tliba2roip1cf

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

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=τ(n^gcd(n, a(n-1)))%8
a(0)=1
gcd(a,b)=greatest common divisor
τ(n)=number of divisors of n
n≥0
8 operations
Prime

Sequence 3bdfdfrgcbnri

1, 1, 2, 2, 5, 6, 1, 2, 7, 3, 4, 2, 15, 2, 9, 16, 17, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=τ(n^(gcd(n, a(n-1))%6))
a(0)=1
gcd(a,b)=greatest common divisor
τ(n)=number of divisors of n
n≥0
8 operations
Prime

Sequence snfwyowdq3rve

1, 1, 2, 2, 5, 6, 1, 3, 3, 7, 7, 11, 13, 13, 15, 2, 5, 4, 7, 8, 7, 10, 11, 14, 19, 20, 16, 20, 16, 20, 28, 29, 1, 3, 5, 3, 5, 7, 7, 9, 11, 9, 15, 13, 13, 11, 19, 27, 27, 25, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=p(n)%(n+ω(τ(a(n-1))))
a(0)=1
p(n)=nth prime
τ(n)=number of divisors of n
ω(n)=number of distinct prime divisors of n
n≥1
8 operations
Prime

Sequence cd33fvga0rldd

1, 1, 2, 2, 5, 6, 1, 7, 3, 10, 1, 11, 13, 14, 1, 15, 2, 6, 13, 10, 11, 22, 1, 23, 5, 26, 1, 3, 29, 30, 31, 2, 33, 1, 34, 2, 37, 38, 1, 39, 2, 42, 43, 22, 23, 46, 1, 47, 7, 10, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n-floor(a(n-1)^λ(a(n-1))))
a(0)=1
λ(n)=Liouville's function
rad(n)=square free kernel of n
n≥1
8 operations
Prime

Sequence 2r5qi1fdanwpe

1, 1, 2, 2, 5, 6, 1, 7, 9, 1, 10, 2, 13, 1, 15, 1, 17, 1, 18, 2, 21, 22, 1, 24, 25, 1, 26, 2, 29, 1, 30, 2, 33, 1, 34, 2, 37, 1, 38, 2, 41, 42, 1, 43, 45, 46, 47, 1, 49, 1, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=n-lcm(μ(3+n), a(n-1))
a(0)=1
μ(n)=Möbius function
lcm(a,b)=least common multiple
n≥1
8 operations
Prime

Sequence uabpt200gwrbi

1, 1, 2, 2, 5, 6, 2, 1, 2, 7, 1, 1, 2, 13, 1, 1, 8, 4, 7, 8, 7, 10, 3, 4, 19, 2, 5, 20, 16, 20, 28, 29, 1, 3, 5, 3, 5, 7, 7, 9, 11, 9, 15, 9, 13, 11, 1, 1, 3, 25, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=p(n)%rad(n+ω(a(n-1)))
a(0)=1
p(n)=nth prime
ω(n)=number of distinct prime divisors of n
rad(n)=square free kernel of n
n≥1
8 operations
Prime

Sequence iz0nxdenha3zn

1, 1, 2, 2, 5, 6, 2, 1, 2, 7, 1, 1, 2, 13, 1, 1, 8, 19, 7, 8, 1, 13, 5, 4, 1, 23, 5, 20, 1, 23, 1, 1, 5, 34, 1, 1, 9, 3, 7, 9, 7, 9, 11, 13, 13, 11, 1, 1, 3, 25, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=p(n)%rad(n+Ω(a(n-1)))
a(0)=1
p(n)=nth prime
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
n≥1
8 operations
Prime

Sequence xhpuzustgo50c

1, 1, 2, 2, 5, 6, 2, 1, 5, 7, 7, 11, 13, 13, 15, 17, 5, 2, 7, 2, 7, 10, 2, 14, 2, 10, 2, 10, 2, 10, 14, 29, 1, 3, 5, 3, 5, 7, 7, 3, 11, 3, 15, 3, 13, 11, 19, 3, 3, 5, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(p(n)%(n+Ω(a(n-1))))
a(0)=1
p(n)=nth prime
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
n≥1
8 operations
Prime

Sequence 0lhufow1mm1vp

1, 1, 2, 2, 5, 6, 2, 2, 1, 9, 5, 6, 14, 1, 14, 1, 16, 6, 20, 5, 21, 5, 5, 6, 6, 13, 1, 13, 29, 30, 33, 1, 32, 34, 36, 1, 36, 9, 9, 10, 42, 14, 14, 5, 1, 45, 6, 1, 6, 5, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(ω(a(n-1))+rad(n))-1
a(0)=1
ω(n)=number of distinct prime divisors of n
rad(n)=square free kernel of n
n≥1
8 operations
Prime

Sequence oe0hindcohikh

1, 1, 2, 2, 5, 6, 2, 2, 1, 9, 12, 2, 13, 14, 16, 5, 5, 6, 20, 12, 5, 22, 4, 1, 4, 13, 1, 13, 29, 30, 33, 1, 32, 38, 36, 9, 38, 9, 40, 13, 41, 42, 45, 4, 16, 9, 6, 1, 6, 5, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(Ω(a(n-1))+rad(n))-1
a(0)=1
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
n≥1
8 operations
Prime

Sequence ukiyxww2aaeqo

1, 1, 2, 2, 5, 6, 2, 2, 2, 2, 2, 6, 2, 6, 2, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 6, 6, 6, 2, 2, 14, 2, 10, 2, 2, 2, 6, 2, 6, 2, 2, 2, 2, 2, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(τ(∑[n²]+τ(a(n-1))))
a(0)=1
∑(a)=partial sums of a
τ(n)=number of divisors of n
rad(n)=square free kernel of n
n≥0
8 operations
Prime

Sequence c2ubhotci2mco

1, 1, 2, 2, 5, 6, 2, 2, 2, 5, 2, 5, 6, 6, 10, 6, 6, 6, 10, 6, 6, 10, 6, 6, 10, 2, 2, 6, 6, 10, 10, 15, 6, 10, 6, 14, 6, 6, 6, 15, 30, 10, 6, 6, 14, 14, 10, 14, 10, 6, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(τ(a(n-1)*τ(∑[n²])))
a(0)=1
∑(a)=partial sums of a
τ(n)=number of divisors of n
rad(n)=square free kernel of n
n≥1
8 operations
Prime

Sequence xonyth50tet3d

1, 1, 2, 2, 5, 6, 2, 2, 2, 10, 6, 6, 14, 14, 2, 15, 17, 6, 10, 10, 22, 23, 6, 6, 3, 26, 14, 29, 30, 30, 33, 2, 2, 33, 6, 37, 38, 38, 10, 41, 43, 42, 15, 22, 46, 47, 6, 6, 10, 10, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n+Ω(τ(n))%a(n-1))
a(0)=1
τ(n)=number of divisors of n
Ω(n)=number of prime divisors of n
rad(n)=square free kernel of n
n≥0
8 operations
Prime

Sequence n0kbjel3lr3ej

1, 1, 2, 2, 5, 6, 2, 2, 3, 2, 11, 6, 14, 14, 15, 17, 17, 6, 10, 22, 23, 22, 5, 6, 26, 26, 3, 26, 29, 30, 2, 2, 33, 35, 35, 6, 38, 38, 39, 41, 41, 42, 22, 46, 47, 46, 7, 10, 51, 51, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(n-(5-a(n-1))%3)
a(0)=1
rad(n)=square free kernel of n
n≥1
8 operations
Prime

Sequence jl3w1bqcry0xk

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

integer, non-monotonic, +-, A000403 (weak, multiple)

a(n)=(a(n-1)+gpf(n))%9-2
a(0)=1
gpf(n)=greatest prime factor of n
n≥1
8 operations
Prime

Sequence ofrhhzchjjrzd

1, 1, 2, 2, 5, 6, 2, 2, 3, 6, 6, 2, 13, 6, 6, 3, 6, 2, 19, 22, 2, 11, 2, 3, 6, 14, 2, 7, 34, 10, 34, 17, 26, 14, 6, 2, 37, 6, 14, 10, 22, 2, 43, 26, 2, 23, 34, 6, 2, 5, more...

integer, non-monotonic, +, A000403 (weak, multiple)

a(n)=rad(gpf(n)-2+gpf(a(n-1)))
a(0)=1
gpf(n)=greatest prime factor of n
rad(n)=square free kernel of n
n≥1
8 operations
Prime

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