Sequence Database

A database with 497817 machine generated integer and decimal sequences.

Displaying the first 100 results.

Sequence 3bmepyefoqlfp

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

integer, non-constant, non-monotonic, +-0, A008683

a(n)=μ(n)
μ(n)=Möbius function
n≥1
2 operations
Prime

Sequence prf3m20mhvu2m

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

integer, non-constant, monotonic, +0, A000007

a(n)=floor(cos(sin(n)))
n≥0
4 operations
N
nSOf
a(n)=floor(sin(a(n-1)))
a(0)=1
n≥0
3 operations
Recursive
rSf
a(n)=μ(n*n)
μ(n)=Möbius function
n≥1
4 operations
Prime
nn*μ
a(n)=Ω(a(n-1))
a(0)=1
Ω(n)=max factorization terms
n≥0
2 operations
PrimeRecursive

Sequence lyu0d1h5rvlyg

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

integer, non-constant, non-monotonic, +-0

a(n)=-μ(n)
μ(n)=Möbius function
n≥1
3 operations
Prime
nμ~

Sequence wvf2svirtnqsi

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(Ω(n))
Ω(n)=max factorization terms
μ(n)=Möbius function
n≥1
3 operations
Prime
nΩμ

Sequence hexbe3joutxph

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

integer, non-constant, periodic, non-monotonic, +0, A010872

a(n)=n%3
n≥0
3 operations
N
n3%
a(n)=floor(sqrt(exp(tan(a(n-1)))))
a(0)=0
n≥0
5 operations
Recursive
rWeQf
a(n)=μ(a(n-1))+1
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
rμ1+

Sequence lpwkkk0i0wvwi

0.5403023059, 0.5403023059, 0.5403023059, 1, 0.5403023059, 0.5403023059, 0.5403023059, 1, 1, 0.5403023059, 0.5403023059, 1, 0.5403023059, 0.5403023059, 0.5403023059, 1, 0.5403023059, 1, 0.5403023059, 1, 0.5403023059, 0.5403023059, 0.5403023059, 1, 1, 0.5403023059, 1, 1, 0.5403023059, 0.5403023059, 0.5403023059, 1, 0.5403023059, 0.5403023059, 0.5403023059, 1, 0.5403023059, 0.5403023059, 0.5403023059, 1, 0.5403023059, 0.5403023059, 0.5403023059, 1, 1, 0.5403023059, 0.5403023059, 1, 1, 1, more...

decimal, non-constant, non-monotonic, +

a(n)=cos(μ(n))
μ(n)=Möbius function
n≥1
3 operations
Prime
nμO

Sequence gezqh4e53xr1d

0.8414709848, -0.8414709848, -0.8414709848, 0, -0.8414709848, 0.8414709848, -0.8414709848, 0, 0, 0.8414709848, -0.8414709848, 0, -0.8414709848, 0.8414709848, 0.8414709848, 0, -0.8414709848, 0, -0.8414709848, 0, 0.8414709848, 0.8414709848, -0.8414709848, 0, 0, 0.8414709848, 0, 0, -0.8414709848, -0.8414709848, -0.8414709848, 0, 0.8414709848, 0.8414709848, 0.8414709848, 0, -0.8414709848, 0.8414709848, 0.8414709848, 0, -0.8414709848, -0.8414709848, -0.8414709848, 0, 0, 0.8414709848, -0.8414709848, 0, 0, 0, more...

decimal, non-constant, non-monotonic, +-0

a(n)=sin(μ(n))
μ(n)=Möbius function
n≥1
3 operations
Prime
nμS

Sequence qh5d0mo2ex3xp

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(τ(n))
τ(n)=number of divisors of n
μ(n)=Möbius function
n≥1
3 operations
Prime
nτμ

Sequence y54gg5hplvokk

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(ϕ(n))
ϕ(n)=Euler's totient function
μ(n)=Möbius function
n≥1
3 operations
Prime
nϕμ

Sequence 04dsdnlkqak4n

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

integer, non-constant, non-monotonic, +0, A008966

a(n)=abs(μ(n))
μ(n)=Möbius function
n≥1
3 operations
Prime
nμ|
a(n)=abs(μ(n+λ(a(n-1))))
a(0)=1
λ(n)=Liouville's function
μ(n)=Möbius function
n≥0
6 operations
PrimeRecursive
nrλ+μ|

Sequence cvd3juomahhhi

1.5574077247, -1.5574077247, -1.5574077247, 0, -1.5574077247, 1.5574077247, -1.5574077247, 0, 0, 1.5574077247, -1.5574077247, 0, -1.5574077247, 1.5574077247, 1.5574077247, 0, -1.5574077247, 0, -1.5574077247, 0, 1.5574077247, 1.5574077247, -1.5574077247, 0, 0, 1.5574077247, 0, 0, -1.5574077247, -1.5574077247, -1.5574077247, 0, 1.5574077247, 1.5574077247, 1.5574077247, 0, -1.5574077247, 1.5574077247, 1.5574077247, 0, -1.5574077247, -1.5574077247, -1.5574077247, 0, 0, 1.5574077247, -1.5574077247, 0, 0, 0, more...

decimal, non-constant, non-monotonic, +-0

a(n)=tan(μ(n))
μ(n)=Möbius function
n≥1
3 operations
Prime
nμW

Sequence abbtp4v3i3flh

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

integer, non-constant, non-monotonic, +-

a(n)=round(sin(tan(abs(a(n-1)))))
a(0)=2
n≥0
5 operations
Recursive
r|WSR
a(n)=μ(abs(a(n-1)))
a(0)=2
μ(n)=Möbius function
n≥0
3 operations
PrimeRecursive
r|μ

Sequence 5shncxf4ukhle

2, 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, non-constant, monotonic, +0, A000038

a(n)=round(tan(exp(-n)))
n≥0
5 operations
N
n~eWR
a(n)=floor(sin(a(n-1)))
a(0)=2
n≥0
3 operations
Recursive
rSf
a(n)=μ(n*n)*2
μ(n)=Möbius function
n≥1
6 operations
Prime
nn*μ2*

Sequence xgf1n3aoayq1

2, 3, 3, 5, 3, 5, 3, 7, 5, 5, 3, 7, 3, 5, 5, 11, 3, 7, 3, 7, 5, 5, 3, 11, 5, 5, 7, 7, 3, 7, 3, 13, 5, 5, 5, 11, 3, 5, 5, 11, 3, 7, 3, 7, 7, 5, 3, 13, 5, 7, more...

integer, non-constant, non-monotonic, +

a(n)=p(Ω(n))
Ω(n)=max factorization terms
p(n)=nth prime
n≥1
3 operations
Prime
nΩp
a(n)=p(Ω(n-μ(a(n-1))))
a(0)=2
μ(n)=Möbius function
Ω(n)=max factorization terms
p(n)=nth prime
n≥0
6 operations
PrimeRecursive
nrμ-Ωp

Sequence i3z5twmd1ztne

2.7182818285, 0.3678794412, 0.3678794412, 1, 0.3678794412, 2.7182818285, 0.3678794412, 1, 1, 2.7182818285, 0.3678794412, 1, 0.3678794412, 2.7182818285, 2.7182818285, 1, 0.3678794412, 1, 0.3678794412, 1, 2.7182818285, 2.7182818285, 0.3678794412, 1, 1, 2.7182818285, 1, 1, 0.3678794412, 0.3678794412, 0.3678794412, 1, 2.7182818285, 2.7182818285, 2.7182818285, 1, 0.3678794412, 2.7182818285, 2.7182818285, 1, 0.3678794412, 0.3678794412, 0.3678794412, 1, 1, 2.7182818285, 0.3678794412, 1, 1, 1, more...

decimal, non-constant, non-monotonic, +

a(n)=exp(μ(n))
μ(n)=Möbius function
n≥1
3 operations
Prime
nμe

Sequence vhbotvpdgojnk

-9, -11, -11, -10, -11, -9, -11, -10, -10, -9, -11, -10, -11, -9, -9, -10, -11, -10, -11, -10, -9, -9, -11, -10, -10, -9, -10, -10, -11, -11, -11, -10, -9, -9, -9, -10, -11, -9, -9, -10, -11, -11, -11, -10, -10, -9, -11, -10, -10, -10, more...

integer, non-constant, non-monotonic, -

a(n)=μ(n)-10
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ10-

Sequence dgfy3fvpfa4dg

-8, -10, -10, -9, -10, -8, -10, -9, -9, -8, -10, -9, -10, -8, -8, -9, -10, -9, -10, -9, -8, -8, -10, -9, -9, -8, -9, -9, -10, -10, -10, -9, -8, -8, -8, -9, -10, -8, -8, -9, -10, -10, -10, -9, -9, -8, -10, -9, -9, -9, more...

integer, non-constant, non-monotonic, -

a(n)=μ(n)-9
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ9-

Sequence csubb45bqreqb

-7, -9, -9, -8, -9, -7, -9, -8, -8, -7, -9, -8, -9, -7, -7, -8, -9, -8, -9, -8, -7, -7, -9, -8, -8, -7, -8, -8, -9, -9, -9, -8, -7, -7, -7, -8, -9, -7, -7, -8, -9, -9, -9, -8, -8, -7, -9, -8, -8, -8, more...

integer, non-constant, non-monotonic, -

a(n)=μ(n)-8
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ8-

Sequence z2tdmua4tx3mh

-6, -8, -8, -7, -8, -6, -8, -7, -7, -6, -8, -7, -8, -6, -6, -7, -8, -7, -8, -7, -6, -6, -8, -7, -7, -6, -7, -7, -8, -8, -8, -7, -6, -6, -6, -7, -8, -6, -6, -7, -8, -8, -8, -7, -7, -6, -8, -7, -7, -7, more...

integer, non-constant, non-monotonic, -

a(n)=μ(n)-7
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ7-

Sequence d1k1svzna2cho

-5, -7, -7, -6, -7, -5, -7, -6, -6, -5, -7, -6, -7, -5, -5, -6, -7, -6, -7, -6, -5, -5, -7, -6, -6, -5, -6, -6, -7, -7, -7, -6, -5, -5, -5, -6, -7, -5, -5, -6, -7, -7, -7, -6, -6, -5, -7, -6, -6, -6, more...

integer, non-constant, non-monotonic, -

a(n)=μ(n)-6
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ6-

Sequence fgkn3pbcjpcjb

-4, -6, -6, -5, -6, -4, -6, -5, -5, -4, -6, -5, -6, -4, -4, -5, -6, -5, -6, -5, -4, -4, -6, -5, -5, -4, -5, -5, -6, -6, -6, -5, -4, -4, -4, -5, -6, -4, -4, -5, -6, -6, -6, -5, -5, -4, -6, -5, -5, -5, more...

integer, non-constant, non-monotonic, -

a(n)=μ(n)-5
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ5-

Sequence b2advy0ihuryk

-3, -5, -5, -4, -5, -3, -5, -4, -4, -3, -5, -4, -5, -3, -3, -4, -5, -4, -5, -4, -3, -3, -5, -4, -4, -3, -4, -4, -5, -5, -5, -4, -3, -3, -3, -4, -5, -3, -3, -4, -5, -5, -5, -4, -4, -3, -5, -4, -4, -4, more...

integer, non-constant, non-monotonic, -

a(n)=μ(n)-4
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ4-

Sequence e5vxullmnsf4p

-2.7182818285, -0.3678794412, -0.3678794412, -1, -0.3678794412, -2.7182818285, -0.3678794412, -1, -1, -2.7182818285, -0.3678794412, -1, -0.3678794412, -2.7182818285, -2.7182818285, -1, -0.3678794412, -1, -0.3678794412, -1, -2.7182818285, -2.7182818285, -0.3678794412, -1, -1, -2.7182818285, -1, -1, -0.3678794412, -0.3678794412, -0.3678794412, -1, -2.7182818285, -2.7182818285, -2.7182818285, -1, -0.3678794412, -2.7182818285, -2.7182818285, -1, -0.3678794412, -0.3678794412, -0.3678794412, -1, -1, -2.7182818285, -0.3678794412, -1, -1, -1, more...

decimal, non-constant, non-monotonic, -

a(n)=-exp(μ(n))
μ(n)=Möbius function
n≥1
4 operations
Prime
nμe~

Sequence eufucbvrcysei

-2.1415926536, -4.1415926536, -4.1415926536, -3.1415926536, -4.1415926536, -2.1415926536, -4.1415926536, -3.1415926536, -3.1415926536, -2.1415926536, -4.1415926536, -3.1415926536, -4.1415926536, -2.1415926536, -2.1415926536, -3.1415926536, -4.1415926536, -3.1415926536, -4.1415926536, -3.1415926536, -2.1415926536, -2.1415926536, -4.1415926536, -3.1415926536, -3.1415926536, -2.1415926536, -3.1415926536, -3.1415926536, -4.1415926536, -4.1415926536, -4.1415926536, -3.1415926536, -2.1415926536, -2.1415926536, -2.1415926536, -3.1415926536, -4.1415926536, -2.1415926536, -2.1415926536, -3.1415926536, -4.1415926536, -4.1415926536, -4.1415926536, -3.1415926536, -3.1415926536, -2.1415926536, -4.1415926536, -3.1415926536, -3.1415926536, -3.1415926536, more...

decimal, non-constant, non-monotonic, -

a(n)=μ(n)-π
μ(n)=Möbius function
Pi (3.141...)
n≥1
4 operations
Prime
nμπ-

Sequence l1sy2vyidgu3i

-2, -4, -4, -3, -4, -2, -4, -3, -3, -2, -4, -3, -4, -2, -2, -3, -4, -3, -4, -3, -2, -2, -4, -3, -3, -2, -3, -3, -4, -4, -4, -3, -2, -2, -2, -3, -4, -2, -2, -3, -4, -4, -4, -3, -3, -2, -4, -3, -3, -3, more...

integer, non-constant, non-monotonic, -

a(n)=μ(n)-3
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ3-

Sequence 5jrc55mw4lkhm

-1.5574077247, 1.5574077247, 1.5574077247, 0, 1.5574077247, -1.5574077247, 1.5574077247, 0, 0, -1.5574077247, 1.5574077247, 0, 1.5574077247, -1.5574077247, -1.5574077247, 0, 1.5574077247, 0, 1.5574077247, 0, -1.5574077247, -1.5574077247, 1.5574077247, 0, 0, -1.5574077247, 0, 0, 1.5574077247, 1.5574077247, 1.5574077247, 0, -1.5574077247, -1.5574077247, -1.5574077247, 0, 1.5574077247, -1.5574077247, -1.5574077247, 0, 1.5574077247, 1.5574077247, 1.5574077247, 0, 0, -1.5574077247, 1.5574077247, 0, 0, 0, more...

decimal, non-constant, non-monotonic, +-0

a(n)=tan(-μ(n))
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ~W

Sequence tkrdqwiqhgx3o

-1, -3, -3, -2, -3, -1, -3, -2, -2, -1, -3, -2, -3, -1, -1, -2, -3, -2, -3, -2, -1, -1, -3, -2, -2, -1, -2, -2, -3, -3, -3, -2, -1, -1, -1, -2, -3, -1, -1, -2, -3, -3, -3, -2, -2, -1, -3, -2, -2, -2, more...

integer, non-constant, non-monotonic, -

a(n)=μ(n)-2
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ2-

Sequence fq5ilsoaoglod

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

integer, non-constant, non-monotonic, -0

a(n)=-abs(μ(n))
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ|~

Sequence xnvfmumfa1bgl

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n+1)
μ(n)=Möbius function
n≥1
4 operations
Prime
n1+μ

Sequence i1lo5tpw1wdln

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(floor(exp(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime
nefμ

Sequence htcbeclnuzt

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(round(exp(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime
neRμ

Sequence fvejnqoyiek1h

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

integer, non-constant, non-monotonic, +-0

a(n)=-μ(ϕ(n))
ϕ(n)=Euler's totient function
μ(n)=Möbius function
n≥1
4 operations
Prime
nϕμ~

Sequence cy5baykfecjmk

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n+2)
μ(n)=Möbius function
n≥1
4 operations
Prime
n2+μ

Sequence 0i1kpcv4qg3ud

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n+10)
μ(n)=Möbius function
n≥1
4 operations
Prime
n10+μ

Sequence qkmpgcfrsk3xj

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n+6)
μ(n)=Möbius function
n≥1
4 operations
Prime
n6+μ

Sequence f2yai1xfzziyn

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

integer, non-constant, non-monotonic, +-0, A099991

a(n)=μ(n+n)
μ(n)=Möbius function
n≥1
4 operations
Prime
nn+μ

Sequence jkz0sfodrk3yk

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(ceil(exp(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime
neTμ

Sequence rh24idczgft5i

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n+4)
μ(n)=Möbius function
n≥1
4 operations
Prime
n4+μ

Sequence xzu34pnpuqctd

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n*3)
μ(n)=Möbius function
n≥1
4 operations
Prime
n3*μ

Sequence kbew0jqc5hynf

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n*5)
μ(n)=Möbius function
n≥1
4 operations
Prime
n5*μ

Sequence ljfqruhb4hufd

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n*7)
μ(n)=Möbius function
n≥1
4 operations
Prime
n7*μ

Sequence m4u1kdhos0zhn

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

integer, non-constant, non-monotonic, +-0

a(n)=-μ(τ(n))
τ(n)=number of divisors of n
μ(n)=Möbius function
n≥1
4 operations
Prime
nτμ~

Sequence 4thdx1cfnzdp

-0.9117339148, 0.9330920756, 0.9330920756, 0.5403023059, 0.9330920756, -0.9117339148, 0.9330920756, 0.5403023059, 0.5403023059, -0.9117339148, 0.9330920756, 0.5403023059, 0.9330920756, -0.9117339148, -0.9117339148, 0.5403023059, 0.9330920756, 0.5403023059, 0.9330920756, 0.5403023059, -0.9117339148, -0.9117339148, 0.9330920756, 0.5403023059, 0.5403023059, -0.9117339148, 0.5403023059, 0.5403023059, 0.9330920756, 0.9330920756, 0.9330920756, 0.5403023059, -0.9117339148, -0.9117339148, -0.9117339148, 0.5403023059, 0.9330920756, -0.9117339148, -0.9117339148, 0.5403023059, 0.9330920756, 0.9330920756, 0.9330920756, 0.5403023059, 0.5403023059, -0.9117339148, 0.9330920756, 0.5403023059, 0.5403023059, 0.5403023059, more...

decimal, non-constant, non-monotonic, +-

a(n)=cos(exp(μ(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime
nμeO

Sequence tgjzmfj4dpg3j

-0.8414709848, 0.8414709848, 0.8414709848, 0, 0.8414709848, -0.8414709848, 0.8414709848, 0, 0, -0.8414709848, 0.8414709848, 0, 0.8414709848, -0.8414709848, -0.8414709848, 0, 0.8414709848, 0, 0.8414709848, 0, -0.8414709848, -0.8414709848, 0.8414709848, 0, 0, -0.8414709848, 0, 0, 0.8414709848, 0.8414709848, 0.8414709848, 0, -0.8414709848, -0.8414709848, -0.8414709848, 0, 0.8414709848, -0.8414709848, -0.8414709848, 0, 0.8414709848, 0.8414709848, 0.8414709848, 0, 0, -0.8414709848, 0.8414709848, 0, 0, 0, more...

decimal, non-constant, non-monotonic, +-0

a(n)=sin(-μ(n))
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ~S

Sequence jxzesvcjbktel

-0.6156264704, -0.6156264704, -0.6156264704, 0, -0.6156264704, -0.6156264704, -0.6156264704, 0, 0, -0.6156264704, -0.6156264704, 0, -0.6156264704, -0.6156264704, -0.6156264704, 0, -0.6156264704, 0, -0.6156264704, 0, -0.6156264704, -0.6156264704, -0.6156264704, 0, 0, -0.6156264704, 0, 0, -0.6156264704, -0.6156264704, -0.6156264704, 0, -0.6156264704, -0.6156264704, -0.6156264704, 0, -0.6156264704, -0.6156264704, -0.6156264704, 0, -0.6156264704, -0.6156264704, -0.6156264704, 0, 0, -0.6156264704, -0.6156264704, 0, 0, 0, more...

decimal, non-constant, non-monotonic, -0

a(n)=ln(cos(μ(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime
nμOl

Sequence ajf0fyv14nxum

-0.5403023059, -0.5403023059, -0.5403023059, -1, -0.5403023059, -0.5403023059, -0.5403023059, -1, -1, -0.5403023059, -0.5403023059, -1, -0.5403023059, -0.5403023059, -0.5403023059, -1, -0.5403023059, -1, -0.5403023059, -1, -0.5403023059, -0.5403023059, -0.5403023059, -1, -1, -0.5403023059, -1, -1, -0.5403023059, -0.5403023059, -0.5403023059, -1, -0.5403023059, -0.5403023059, -0.5403023059, -1, -0.5403023059, -0.5403023059, -0.5403023059, -1, -0.5403023059, -0.5403023059, -0.5403023059, -1, -1, -0.5403023059, -0.5403023059, -1, -1, -1, more...

decimal, non-constant, non-monotonic, -

a(n)=-cos(μ(n))
μ(n)=Möbius function
n≥1
4 operations
Prime
nμO~

Sequence ysqil2cnhv4yp

-0.4505495341, 0.3854255918, 0.3854255918, 1.5574077247, 0.3854255918, -0.4505495341, 0.3854255918, 1.5574077247, 1.5574077247, -0.4505495341, 0.3854255918, 1.5574077247, 0.3854255918, -0.4505495341, -0.4505495341, 1.5574077247, 0.3854255918, 1.5574077247, 0.3854255918, 1.5574077247, -0.4505495341, -0.4505495341, 0.3854255918, 1.5574077247, 1.5574077247, -0.4505495341, 1.5574077247, 1.5574077247, 0.3854255918, 0.3854255918, 0.3854255918, 1.5574077247, -0.4505495341, -0.4505495341, -0.4505495341, 1.5574077247, 0.3854255918, -0.4505495341, -0.4505495341, 1.5574077247, 0.3854255918, 0.3854255918, 0.3854255918, 1.5574077247, 1.5574077247, -0.4505495341, 0.3854255918, 1.5574077247, 1.5574077247, 1.5574077247, more...

decimal, non-constant, non-monotonic, +-

a(n)=tan(exp(μ(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime
nμeW

Sequence kjs3tfgjesiue

0, -3, -4, -4, -6, -5, -8, -8, -9, -9, -12, -12, -14, -13, -14, -16, -18, -18, -20, -20, -20, -21, -24, -24, -25, -25, -27, -28, -30, -31, -32, -32, -32, -33, -34, -36, -38, -37, -38, -40, -42, -43, -44, -44, -45, -45, -48, -48, -49, -50, more...

integer, non-constant, non-monotonic, -0

a(n)=μ(n)-n
μ(n)=Möbius function
n≥1
4 operations
Prime
nμn-

Sequence xbr1rt25tzwrd

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

integer, non-constant, non-monotonic, -0

a(n)=μ(n)-1
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ1-

Sequence 4oafitaxoswxc

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

integer, non-constant, periodic, non-monotonic, -0

a(n)=-n%3
n≥0
4 operations
N
n~3%
a(n)=(a(n-1)-1)%3
a(0)=0
n≥0
5 operations
Recursive
r1-3%
a(n)=-μ(-a(n-1))-1
a(0)=0
μ(n)=Möbius function
n≥0
6 operations
PrimeRecursive
r~μ~1-

Sequence d2jup5sigy2ti

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

integer, non-constant, non-monotonic, -0

a(n)=floor(sin(μ(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime
nμSf

Sequence vipqa1tap3rjf

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n)%n
μ(n)=Möbius function
n≥1
4 operations
Prime
nμn%

Sequence cog3mb2jbqozd

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

integer, non-constant, non-monotonic, +-0

a(n)=-μ(Ω(n))
Ω(n)=max factorization terms
μ(n)=Möbius function
n≥1
4 operations
Prime
nΩμ~

Sequence wbfnrfdh2yrae

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

integer, non-constant, non-monotonic, +-0

a(n)=a(n-1)-μ(n)
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
rnμ-

Sequence afqc3py11l5lm

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n+3)
μ(n)=Möbius function
n≥1
4 operations
Prime
n3+μ

Sequence 1vzqqmxecqoyj

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

integer, non-constant, non-monotonic, +-0

a(n)=-a(n-1)^a(n-1)
a(0)=0
n≥0
4 operations
Recursive
rr^~
a(n)=μ(a(n-1)+2)
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
r2+μ

Sequence zbg4defdulp0i

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, non-constant, periodic, non-monotonic, +-0

a(n)=μ(a(n-1)+7)
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
r7+μ

Sequence lisu1oxwzfdci

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

integer, non-constant, non-monotonic, +0, A107078

a(n)=floor(cos(μ(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime
nμOf

Sequence ruak1y3pmaqlp

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(Ω(Ω(n)))
Ω(n)=max factorization terms
μ(n)=Möbius function
n≥1
4 operations
Prime
nΩΩμ

Sequence c4phwngxndlne

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n+7)
μ(n)=Möbius function
n≥1
4 operations
Prime
n7+μ

Sequence ws4uuhpzllwno

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(floor(Λ(n)))
Λ(n)=Von Mangoldt's function
μ(n)=Möbius function
n≥1
4 operations
Prime
nΛfμ

Sequence mxmj30h0adkse

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(Ω(ϕ(n)))
ϕ(n)=Euler's totient function
Ω(n)=max factorization terms
μ(n)=Möbius function
n≥1
4 operations
Prime
nϕΩμ

Sequence f1x4wzbbmhmwe

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(floor(ln(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime
nlfμ

Sequence m1c2neihhylui

0, 0.8414709848, 0.8414709848, -0.8414709848, 0.8414709848, -0.8414709848, 0.8414709848, -0.8414709848, -0.8414709848, -0.8414709848, 0.8414709848, -0.8414709848, 0.8414709848, -0.8414709848, -0.8414709848, 0, 0.8414709848, -0.8414709848, 0.8414709848, -0.8414709848, -0.8414709848, -0.8414709848, 0.8414709848, 0, -0.8414709848, -0.8414709848, -0.8414709848, -0.8414709848, 0.8414709848, -0.8414709848, 0.8414709848, -0.8414709848, -0.8414709848, -0.8414709848, -0.8414709848, 0, 0.8414709848, -0.8414709848, -0.8414709848, 0, 0.8414709848, -0.8414709848, 0.8414709848, -0.8414709848, -0.8414709848, -0.8414709848, 0.8414709848, -0.8414709848, -0.8414709848, -0.8414709848, more...

decimal, non-constant, non-monotonic, +-0

a(n)=sin(μ(Ω(n)))
Ω(n)=max factorization terms
μ(n)=Möbius function
n≥1
4 operations
Prime
nΩμS

Sequence vmdfceddxtds

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n)-a(n-1)
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
nμr-

Sequence 0pe5q3gypoo4j

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(ceil(ln(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime
nlTμ

Sequence bwt5rnpd4vili

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n+a(n-1))
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
nr+μ

Sequence n5dohrs2pvmdp

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n-1)
μ(n)=Möbius function
n≥1
4 operations
Prime
n1-μ

Sequence rrghl0etpztnh

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n+8)
μ(n)=Möbius function
n≥1
4 operations
Prime
n8+μ

Sequence gmholsdphph2e

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, non-constant, periodic, non-monotonic, +-0, A102283

a(n)=-a(n-1)-a(n-2)
a(0)=0
a(1)=1
n≥0
4 operations
Recursive
r~s-
a(n)=μ(a(n-1)+1)
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
r1+μ

Sequence szmkizu0ybrpo

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(ceil(Λ(n)))
Λ(n)=Von Mangoldt's function
μ(n)=Möbius function
n≥1
4 operations
Prime
nΛTμ

Sequence ewtlm2cqekion

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n)+a(n-1)
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
nμr+

Sequence y2qi0lgdavsoh

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(n-a(n-1))
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
nr-μ

Sequence pbhoa0hupgyq

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(round(ln(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime
nlRμ

Sequence afanhpnwgxcvi

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(round(Λ(n)))
Λ(n)=Von Mangoldt's function
μ(n)=Möbius function
n≥1
4 operations
Prime
nΛRμ

Sequence xpmvb5bmgtjop

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(Ω(τ(n)))
τ(n)=number of divisors of n
Ω(n)=max factorization terms
μ(n)=Möbius function
n≥1
4 operations
Prime
nτΩμ

Sequence yxw01i4f4zcth

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

integer, non-constant, non-monotonic, +-0

a(n)=μ(ϕ(Ω(n)))
Ω(n)=max factorization terms
ϕ(n)=Euler's totient function
μ(n)=Möbius function
n≥1
4 operations
Prime
nΩϕμ

Sequence kz13hzeuuxzy

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

integer, non-constant, non-monotonic, +0

a(n)=abs(μ(Ω(n)))
Ω(n)=max factorization terms
μ(n)=Möbius function
n≥1
4 operations
Prime
nΩμ|

Sequence 541ebmzuzmtul

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

integer, non-constant, periodic, non-monotonic, +0

a(n)=a(n-1)+μ(a(n-2))
a(0)=0
a(1)=1
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
rsμ+

Sequence oldfqzhn5mnnp

0, 1, 1, 2, 5, 6, 5, 8, 8, 9, 10, 10, 11, 14, 13, 16, 16, 17, 19, 20, 20, 21, 21, 22, 23, 26, 25, 27, 28, 29, 31, 32, 32, 33, 33, 34, 35, 36, 38, 38, 39, 40, 42, 44, 44, 45, 46, 46, 47, 50, more...

integer, non-constant, non-monotonic, +0

a(n)=n-μ(a(n-1))
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
nrμ-

Sequence itj0lqjj5i03h

0, 1, 3, 2, 3, 4, 6, 8, 8, 9, 10, 12, 12, 13, 13, 14, 17, 16, 18, 19, 19, 20, 22, 24, 24, 25, 26, 28, 28, 29, 29, 30, 31, 32, 34, 36, 36, 37, 37, 38, 41, 40, 42, 42, 43, 44, 46, 48, 48, 49, more...

integer, non-constant, non-monotonic, +0

a(n)=n+μ(a(n-1))
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
nrμ+

Sequence xu54t0f1m5bfo

0, 1.5574077247, 1.5574077247, -1.5574077247, 1.5574077247, -1.5574077247, 1.5574077247, -1.5574077247, -1.5574077247, -1.5574077247, 1.5574077247, -1.5574077247, 1.5574077247, -1.5574077247, -1.5574077247, 0, 1.5574077247, -1.5574077247, 1.5574077247, -1.5574077247, -1.5574077247, -1.5574077247, 1.5574077247, 0, -1.5574077247, -1.5574077247, -1.5574077247, -1.5574077247, 1.5574077247, -1.5574077247, 1.5574077247, -1.5574077247, -1.5574077247, -1.5574077247, -1.5574077247, 0, 1.5574077247, -1.5574077247, -1.5574077247, 0, 1.5574077247, -1.5574077247, 1.5574077247, -1.5574077247, -1.5574077247, -1.5574077247, 1.5574077247, -1.5574077247, -1.5574077247, -1.5574077247, more...

decimal, non-constant, non-monotonic, +-0

a(n)=tan(μ(Ω(n)))
Ω(n)=max factorization terms
μ(n)=Möbius function
n≥1
4 operations
Prime
nΩμW

Sequence 51p3ceon04usl

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

integer, non-constant, non-monotonic, +0

a(n)=1-μ(n)
μ(n)=Möbius function
n≥1
4 operations
Prime
1nμ-

Sequence kyfi2dqogoad

0, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, more...

integer, non-constant, non-monotonic, +0

a(n)=ceil(sin(a(n-1)))+3
a(0)=0
n≥0
5 operations
Recursive
rST3+
a(n)=3-μ(a(n-1))
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
3rμ-

Sequence pj5siarkzmf4p

0, 3, 4, 4, 6, 5, 8, 8, 9, 9, 12, 12, 14, 13, 14, 16, 18, 18, 20, 20, 20, 21, 24, 24, 25, 25, 27, 28, 30, 31, 32, 32, 32, 33, 34, 36, 38, 37, 38, 40, 42, 43, 44, 44, 45, 45, 48, 48, 49, 50, more...

integer, non-constant, non-monotonic, +0

a(n)=n-μ(n)
μ(n)=Möbius function
n≥1
4 operations
Prime
nnμ-

Sequence tneuexr30s1pd

0, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, more...

integer, non-constant, non-monotonic, +0

a(n)=5-a(n-1)%2
a(0)=0
n≥0
5 operations
Recursive
5r2%-
a(n)=μ(a(n-1))+5
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
rμ5+

Sequence ynuinanwozvfk

0, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, 6, 4, 5, more...

integer, non-constant, non-monotonic, +0

a(n)=5-μ(a(n-1))
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
5rμ-

Sequence f5pdog5yl1tll

0, 6, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, more...

integer, non-constant, non-monotonic, +0

a(n)=6-μ(a(n-1))
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
6rμ-

Sequence wkv3i0rpmit4i

0, 6, 7, 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, non-constant, non-monotonic, +0

a(n)=μ(a(n-1))+6
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
rμ6+

Sequence ov1qd5lyij5mf

0, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, 6, 8, 7, more...

integer, non-constant, non-monotonic, +0

a(n)=μ(a(n-1))+7
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
rμ7+

Sequence rf0ua0qg3y31m

0, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, more...

integer, non-constant, non-monotonic, +0

a(n)=a(n-1)%2+7
a(0)=0
n≥0
5 operations
Recursive
r2%7+
a(n)=7-μ(a(n-1))
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
7rμ-

Sequence gqb4v2vrb313c

0, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, 9, 10, more...

integer, non-constant, non-monotonic, +0

a(n)=floor(sin(a(n-1)))+10
a(0)=0
n≥0
5 operations
Recursive
rSf10+
a(n)=10-μ(a(n-1))
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
10rμ-

Sequence mle5qmdcjtove

0, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, 11, 9, 10, more...

integer, non-constant, non-monotonic, +0

a(n)=μ(a(n-1))+10
a(0)=0
μ(n)=Möbius function
n≥0
4 operations
PrimeRecursive
rμ10+

Sequence cntmymcnvickm

0.0133882021, 0.0133882021, 0.0133882021, 1, 0.0133882021, 0.0133882021, 0.0133882021, 1, 1, 0.0133882021, 0.0133882021, 1, 0.0133882021, 0.0133882021, 0.0133882021, 1, 0.0133882021, 1, 0.0133882021, 1, 0.0133882021, 0.0133882021, 0.0133882021, 1, 1, 0.0133882021, 1, 1, 0.0133882021, 0.0133882021, 0.0133882021, 1, 0.0133882021, 0.0133882021, 0.0133882021, 1, 0.0133882021, 0.0133882021, 0.0133882021, 1, 0.0133882021, 0.0133882021, 0.0133882021, 1, 1, 0.0133882021, 0.0133882021, 1, 1, 1, more...

decimal, non-constant, non-monotonic, +

a(n)=cos(tan(μ(n)))
μ(n)=Möbius function
n≥1
4 operations
Prime
nμWO

Sequence amiudjv3ukjcg

0.1, -0.1, -0.1, 0, -0.1, 0.1, -0.1, 0, 0, 0.1, -0.1, 0, -0.1, 0.1, 0.1, 0, -0.1, 0, -0.1, 0, 0.1, 0.1, -0.1, 0, 0, 0.1, 0, 0, -0.1, -0.1, -0.1, 0, 0.1, 0.1, 0.1, 0, -0.1, 0.1, 0.1, 0, -0.1, -0.1, -0.1, 0, 0, 0.1, -0.1, 0, 0, 0, more...

decimal, non-constant, non-monotonic, +-0

a(n)=μ(n)/10
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ10/

Sequence axxnfrltepjhb

0.1111111111, -0.1111111111, -0.1111111111, 0, -0.1111111111, 0.1111111111, -0.1111111111, 0, 0, 0.1111111111, -0.1111111111, 0, -0.1111111111, 0.1111111111, 0.1111111111, 0, -0.1111111111, 0, -0.1111111111, 0, 0.1111111111, 0.1111111111, -0.1111111111, 0, 0, 0.1111111111, 0, 0, -0.1111111111, -0.1111111111, -0.1111111111, 0, 0.1111111111, 0.1111111111, 0.1111111111, 0, -0.1111111111, 0.1111111111, 0.1111111111, 0, -0.1111111111, -0.1111111111, -0.1111111111, 0, 0, 0.1111111111, -0.1111111111, 0, 0, 0, more...

decimal, non-constant, non-monotonic, +-0

a(n)=μ(n)/9
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ9/

Sequence xgzzty4likcqk

0.125, -0.125, -0.125, 0, -0.125, 0.125, -0.125, 0, 0, 0.125, -0.125, 0, -0.125, 0.125, 0.125, 0, -0.125, 0, -0.125, 0, 0.125, 0.125, -0.125, 0, 0, 0.125, 0, 0, -0.125, -0.125, -0.125, 0, 0.125, 0.125, 0.125, 0, -0.125, 0.125, 0.125, 0, -0.125, -0.125, -0.125, 0, 0, 0.125, -0.125, 0, 0, 0, more...

decimal, non-constant, non-monotonic, +-0

a(n)=μ(n)/8
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ8/

Sequence pqsfbdi13rl1b

0.1428571429, -0.1428571429, -0.1428571429, 0, -0.1428571429, 0.1428571429, -0.1428571429, 0, 0, 0.1428571429, -0.1428571429, 0, -0.1428571429, 0.1428571429, 0.1428571429, 0, -0.1428571429, 0, -0.1428571429, 0, 0.1428571429, 0.1428571429, -0.1428571429, 0, 0, 0.1428571429, 0, 0, -0.1428571429, -0.1428571429, -0.1428571429, 0, 0.1428571429, 0.1428571429, 0.1428571429, 0, -0.1428571429, 0.1428571429, 0.1428571429, 0, -0.1428571429, -0.1428571429, -0.1428571429, 0, 0, 0.1428571429, -0.1428571429, 0, 0, 0, more...

decimal, non-constant, non-monotonic, +-0

a(n)=μ(n)/7
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ7/

Sequence k0ww5n35okcbi

0.1666666667, -0.1666666667, -0.1666666667, 0, -0.1666666667, 0.1666666667, -0.1666666667, 0, 0, 0.1666666667, -0.1666666667, 0, -0.1666666667, 0.1666666667, 0.1666666667, 0, -0.1666666667, 0, -0.1666666667, 0, 0.1666666667, 0.1666666667, -0.1666666667, 0, 0, 0.1666666667, 0, 0, -0.1666666667, -0.1666666667, -0.1666666667, 0, 0.1666666667, 0.1666666667, 0.1666666667, 0, -0.1666666667, 0.1666666667, 0.1666666667, 0, -0.1666666667, -0.1666666667, -0.1666666667, 0, 0, 0.1666666667, -0.1666666667, 0, 0, 0, more...

decimal, non-constant, non-monotonic, +-0

a(n)=μ(n)/6
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ6/

Sequence qhxgff2knkdno

0.2, -0.2, -0.2, 0, -0.2, 0.2, -0.2, 0, 0, 0.2, -0.2, 0, -0.2, 0.2, 0.2, 0, -0.2, 0, -0.2, 0, 0.2, 0.2, -0.2, 0, 0, 0.2, 0, 0, -0.2, -0.2, -0.2, 0, 0.2, 0.2, 0.2, 0, -0.2, 0.2, 0.2, 0, -0.2, -0.2, -0.2, 0, 0, 0.2, -0.2, 0, 0, 0, more...

decimal, non-constant, non-monotonic, +-0

a(n)=μ(n)/5
μ(n)=Möbius function
n≥1
4 operations
Prime
nμ5/