Sequence Database

A database with 2076264 machine generated integer and decimal sequences.

Displaying result 0-99 of total 28451. [0] [1] [2] [3] [4] ... [284]

Sequence nfg4ocm1ms2ao

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

integer, monotonic, +, A110654

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

Sequence vyfek0l5mu4rf

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, 25, 26, more...

integer, monotonic, +, A080513

a(n)=n-a(n-1)
a(0)=1
n≥2
3 operations
Recursive
a(n)=ceil(n/2)
n≥2
4 operations
Arithmetic
a(n)=ceil(cosh(log(n)))
n≥1
4 operations
Trigonometric
a(n)=ceil(sinh(log(n)))
n≥2
4 operations
Trigonometric
a(n)=and(31, n-a(n-1))
a(0)=1
and(a,b)=bitwise and
n≥2
5 operations
Recursive

Sequence qcndhwgq3am2m

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

integer, monotonic, +, A178487

a(n)=ceil(n/31)
n≥0
4 operations
Arithmetic
a(n)=floor(root(5, n))
root(n,a)=the n-th root of a
n≥0
4 operations
Power
a(n)=stern(floor(root(π, n)))
π Pi=3.1415... (Pi)
root(n,a)=the n-th root of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Recursive
a(n)=ω(ceil(∑[ϕ/n]))
ϕ GoldenRatio=1.618... (Golden Ratio)
∑(a)=partial sums of a
ω(n)=number of distinct prime divisors of n
n≥2
6 operations
Prime
a(n)=ceil(Λ(ceil(root(5, n))))
root(n,a)=the n-th root of a
Λ(n)=Von Mangoldt's function
n≥1
6 operations
Prime

Sequence mrgix3ug41pgj

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

integer, monotonic, +, A231560

a(n)=ceil(n/25)
n≥0
4 operations
Arithmetic
a(n)=round(root(8, n))
root(n,a)=the n-th root of a
n≥0
4 operations
Power
a(n)=ceil(n/zetazero(2))
zetazero(n)=non trivial zeros of Riemann zeta
n≥0
5 operations
Prime
a(n)=stern(floor(n^Pólya_D3))
Pólya_D3=0.3405... (Pólya random walk 3D)
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Recursive
a(n)=ceil(log(P(n))/8)
P(n)=partition numbers
n≥1
6 operations
Combinatoric

Sequence ciwm1xn4ygsse

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

integer, monotonic, +

a(n)=ceil(n/10)
n≥0
4 operations
Arithmetic
a(n)=∑[char[10+a(n-1)]]
a(0)=1
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence 5idot4ai0qxle

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

integer, monotonic, +

a(n)=ceil(n/9)
n≥0
4 operations
Arithmetic
a(n)=∑[char[9+a(n-1)]]
a(0)=1
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=ceil(n*(1/3)²)
n≥0
7 operations
Power

Sequence xkeiqet1m0eug

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

integer, monotonic, +, A110656

a(n)=ceil(n/8)
n≥0
4 operations
Arithmetic
a(n)=ceil(n/sqrt(65))
n≥0
5 operations
Power
a(n)=∑[char[8+a(n-1)]]
a(0)=1
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[char[or(7, n)-6]]
or(a,b)=bitwise or
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
7 operations
Bitwise
a(n)=floor(∑[a(n-2)^a(n-1)/4])
a(0)=0
a(1)=1
∑(a)=partial sums of a
n≥0
7 operations
Recursive

Sequence jocfguk0f1iuj

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

integer, monotonic, +

a(n)=ceil(n/7)
n≥0
4 operations
Arithmetic
a(n)=∑[char[7+a(n-1)]]
a(0)=1
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence jpryscogjiceh

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

integer, monotonic, +

a(n)=ceil(n/6)
n≥0
4 operations
Arithmetic
a(n)=∑[char[6+a(n-1)]]
a(0)=1
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence bgqfxs0u23mz

0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, more...

integer, monotonic, +

a(n)=ceil(n/5)
n≥0
4 operations
Arithmetic
a(n)=ceil(n/exp(ϕ))
ϕ GoldenRatio=1.618... (Golden Ratio)
n≥0
5 operations
Power
a(n)=∑[char[5+a(n-1)]]
a(0)=1
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence j5zosyegvg0bd

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

integer, monotonic, +, A110655

a(n)=ceil(n/4)
n≥0
4 operations
Arithmetic
a(n)=round(n/log(51))
n≥1
5 operations
Power
a(n)=∑[char[4+a(n-1)]]
a(0)=1
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=round(xor(1, n)/4)
xor(a,b)=bitwise exclusive or
n≥1
6 operations
Bitwise
a(n)=round(n/4)%n
n≥1
6 operations
Divisibility

Sequence ns21xiwvc0apm

0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, more...

integer, monotonic, +

a(n)=ceil(n/3)
n≥0
4 operations
Arithmetic
a(n)=ceil(n*γ²)
γ EulerGamma=0.5772... (Euler Gamma)
n≥0
5 operations
Power
a(n)=∑[char[3+a(n-1)]]
a(0)=1
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=n-a(n-1)-a(n-2)
a(0)=0
a(1)=1
n≥0
5 operations
Recursive
a(n)=∑[C(-a(n-1), a(n-2))]
a(0)=0
a(1)=1
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric

Sequence vdcxqmlxvlacg

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, 2, 2, more...

integer, monotonic, +, A032548

a(n)=ceil(n/48)
n≥1
4 operations
Arithmetic
a(n)=agc(and(48, n))
and(a,b)=bitwise and
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
4 operations
Prime
a(n)=ceil((n/48)²)
n≥1
5 operations
Power
a(n)=stern(ceil(n/24))
stern(n)=Stern-Brocot sequence
n≥1
5 operations
Recursive
a(n)=pt(floor(n/12))
pt(n)=Pascals triangle by rows
n≥0
5 operations
Combinatoric

Sequence afkqmxy424zai

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, 2, 2, 2, more...

integer, monotonic, +, A214956

a(n)=ceil(n/47)
n≥1
4 operations
Arithmetic
a(n)=agc(and(48, n))
and(a,b)=bitwise and
agc(n)=number of factorizations into prime powers (abelian group count)
n≥1
4 operations
Prime
a(n)=ceil((n/47)²)
n≥1
5 operations
Power
a(n)=stern(ceil(n/24))
stern(n)=Stern-Brocot sequence
n≥2
5 operations
Recursive
a(n)=pt(floor(n/12))
pt(n)=Pascals triangle by rows
n≥1
5 operations
Combinatoric

Sequence 5v0ublu21vmqd

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

integer, monotonic, +, A153675

a(n)=ceil(n/40)
n≥1
4 operations
Arithmetic
a(n)=ceil((n/40)²)
n≥1
5 operations
Power
a(n)=stern(ceil(n/20))
stern(n)=Stern-Brocot sequence
n≥1
5 operations
Recursive
a(n)=pt(floor(n/10))
pt(n)=Pascals triangle by rows
n≥0
5 operations
Combinatoric
a(n)=floor(n/20)!
n≥0
5 operations
Combinatoric

Sequence htaqkpqgp0f4p

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

integer, monotonic, +, A032545

a(n)=ceil(n/35)
n≥1
4 operations
Arithmetic
a(n)=ceil(sqrt(n/35))
n≥1
5 operations
Power
a(n)=stern(ceil(n/18))
stern(n)=Stern-Brocot sequence
n≥2
5 operations
Recursive
a(n)=floor(n/18)!
n≥1
5 operations
Combinatoric
a(n)=P(floor(n/18))
P(n)=partition numbers
n≥1
5 operations
Combinatoric

Sequence 520zjfpp3qzcp

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

integer, monotonic, +, A287091

a(n)=ceil(n/27)
n≥1
4 operations
Arithmetic
a(n)=ceil(sqrt(n/27))
n≥1
5 operations
Power
a(n)=ceil(n/26)!
n≥0
5 operations
Combinatoric
a(n)=P(ceil(n/26))
P(n)=partition numbers
n≥0
5 operations
Combinatoric
a(n)=catalan(ceil(n/26))
catalan(n)=the catalan numbers
n≥0
5 operations
Combinatoric

Sequence 430yvndxrurrf

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

integer, monotonic, +, A279759

a(n)=ceil(n/20)
n≥1
4 operations
Arithmetic
a(n)=ceil(n/exp(3))
n≥1
5 operations
Power
a(n)=∑[char[lcm(n, 20)]]
lcm(a,b)=least common multiple
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑[char[20+a(n-1)]]
a(0)=0
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=P(ceil(n/exp(3)))
P(n)=partition numbers
n≥1
6 operations
Combinatoric

Sequence n3s3ol0mtx3mi

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

integer, monotonic, +, A046042

a(n)=ceil(n/16)
n≥2
4 operations
Arithmetic
a(n)=ceil(n/root(γ, 5))
γ EulerGamma=0.5772... (Euler Gamma)
root(n,a)=the n-th root of a
n≥2
6 operations
Power
a(n)=τ(stern(∏[stern(agc(n))]))
agc(n)=number of factorizations into prime powers (abelian group count)
stern(n)=Stern-Brocot sequence
∏(a)=partial products of a
τ(n)=number of divisors of n
n≥0
6 operations
Prime
a(n)=-floor((a(n-1)-n)/15)
a(0)=1
n≥2
7 operations
Recursive
a(n)=∑[stern(stern(agc(n)))]-n
agc(n)=number of factorizations into prime powers (abelian group count)
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
7 operations
Prime

Sequence lmct1ahc1v1jj

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

integer, monotonic, +, A206244

a(n)=ceil(n/11)
n≥1
4 operations
Arithmetic
a(n)=∑[char[lcm(n, 11)]]
lcm(a,b)=least common multiple
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑[char[11+a(n-1)]]
a(0)=0
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=ceil(n/root(γ, 4))
γ EulerGamma=0.5772... (Euler Gamma)
root(n,a)=the n-th root of a
n≥1
6 operations
Power
a(n)=∑[ω(gcd(n, 11)²)]
gcd(a,b)=greatest common divisor
ω(n)=number of distinct prime divisors of n
∑(a)=partial sums of a
n≥0
6 operations
Prime

Sequence hl11gcwi0glxp

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

integer, monotonic, +, A132272

a(n)=ceil(n/10)
n≥1
4 operations
Arithmetic
a(n)=∑[char[lcm(n, 10)]]
lcm(a,b)=least common multiple
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑[char[10+a(n-1)]]
a(0)=0
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=ceil(or(1, n)/10)
or(a,b)=bitwise or
n≥0
6 operations
Bitwise
a(n)=∑[char[10*stern(n)]]
stern(n)=Stern-Brocot sequence
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence mdeholalekit

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

integer, monotonic, +, A133879

a(n)=ceil(n/9)
n≥1
4 operations
Arithmetic
a(n)=ceil(n/sqrt(82))
n≥1
5 operations
Power
a(n)=∑[char[lcm(n, 9)]]
lcm(a,b)=least common multiple
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑[char[9+a(n-1)]]
a(0)=0
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[char[9*stern(n)]]
stern(n)=Stern-Brocot sequence
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence dcbbg024mwlel

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

integer, monotonic, +, A133878

a(n)=ceil(n/8)
n≥1
4 operations
Arithmetic
a(n)=∑[char[and(56, n)]]
and(a,b)=bitwise and
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Bitwise
a(n)=ceil(n/sqrt(65))
n≥1
5 operations
Power
a(n)=∑[char[lcm(n, 8)]]
lcm(a,b)=least common multiple
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑[char[8+a(n-1)]]
a(0)=0
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence 12oc35qlav2wd

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

integer, monotonic, +, A097992

a(n)=ceil(n/6)
n≥1
4 operations
Arithmetic
a(n)=ceil(n/sqrt(37))
n≥1
5 operations
Power
a(n)=∑[char[lcm(n, 6)]]
lcm(a,b)=least common multiple
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑[char[6+a(n-1)]]
a(0)=0
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=ceil(or(1, n)/6)
or(a,b)=bitwise or
n≥0
6 operations
Bitwise

Sequence nwyt4nvan21zb

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

integer, monotonic, +, A008621

a(n)=ceil(n/4)
n≥1
4 operations
Arithmetic
a(n)=∑[char[and(60, n)]]
and(a,b)=bitwise and
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Bitwise
a(n)=round(n/log(51))
n≥2
5 operations
Power
a(n)=∑[char[lcm(n, 4)]]
lcm(a,b)=least common multiple
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑[char[4+a(n-1)]]
a(0)=0
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence e4lxhlta53aj

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

integer, monotonic, +, A144075

a(n)=ceil(n/4)
n≥2
4 operations
Arithmetic
a(n)=ceil(n/log(51))
n≥1
5 operations
Power
a(n)=ceil(or(1, n)/4)
or(a,b)=bitwise or
n≥1
6 operations
Bitwise
a(n)=ceil((n+a(n-1))/5)
a(0)=1
n≥2
6 operations
Recursive
a(n)=ceil(n/log(zetazero(10)))
zetazero(n)=non trivial zeros of Riemann zeta
n≥1
6 operations
Prime

Sequence q55wtjds10w4

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, more...

integer, monotonic, +, A008620

a(n)=ceil(n/3)
n≥1
4 operations
Arithmetic
a(n)=round(n/log(20))
n≥2
5 operations
Power
a(n)=∑[char[lcm(n, 3)]]
lcm(a,b)=least common multiple
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑[char[3+a(n-1)]]
a(0)=0
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=n-a(n-1)-a(n-2)
a(0)=1
a(1)=1
n≥1
5 operations
Recursive

Sequence vqhewa5ijfgji

1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, more...

integer, monotonic, +, A086161

a(n)=ceil(n/3)
n≥2
4 operations
Arithmetic
a(n)=ceil(n/log(19))
n≥1
5 operations
Power
a(n)=n-a(n-1)-a(n-2)
a(0)=1
a(1)=1
n≥2
5 operations
Recursive
a(n)=ceil((n+a(n-1))/4)
a(0)=1
n≥2
6 operations
Recursive
a(n)=ceil(n/log(zetazero(1)))
zetazero(n)=non trivial zeros of Riemann zeta
n≥2
6 operations
Prime

Sequence wtenbuhpylzpp

7, 4, 3, 2, 2, 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, more...

integer, monotonic, +

a(n)=ceil(7/n)
n≥1
4 operations
Arithmetic

Sequence x0dwelekcpmal

8, 4, 3, 2, 2, 2, 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, more...

integer, monotonic, +

a(n)=ceil(8/n)
n≥1
4 operations
Arithmetic
a(n)=ceil(e²/n)
e=2.7182... (Euler e)
n≥1
5 operations
Power

Sequence wlavwij20g3qc

9, 5, 3, 3, 2, 2, 2, 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, more...

integer, monotonic, +

a(n)=ceil(9/n)
n≥1
4 operations
Arithmetic
a(n)=ceil(n*(3/n)²)
n≥1
7 operations
Power

Sequence xhkxrrjji3iyc

10, 5, 4, 3, 2, 2, 2, 2, 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, more...

integer, monotonic, +

a(n)=ceil(10/n)
n≥1
4 operations
Arithmetic
a(n)=ceil(π²/n)
π Pi=3.1415... (Pi)
n≥1
5 operations
Power

Sequence c0mor34r0kh0

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

integer, monotonic, +, A300763

a(n)=ceil(n*CopelandErdős)
CopelandErdős=0.2357... (Copeland-Erdős)
n≥0
4 operations
Arithmetic
a(n)=ceil(n/sqrt(18))
n≥0
5 operations
Power
a(n)=ceil(∑[1/(4+a(n-1))])
a(0)=0
∑(a)=partial sums of a
n≥0
7 operations
Recursive

Sequence 0uxsqpezzbvdo

0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, more...

integer, monotonic, +

a(n)=ceil(n/π)
π Pi=3.1415... (Pi)
n≥0
4 operations
Arithmetic

Sequence 5huhbandty00

0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 19, more...

integer, monotonic, +

a(n)=ceil(n/e)
e=2.7182... (Euler e)
n≥0
4 operations
Arithmetic

Sequence jaeok1a1ud5r

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

integer, monotonic, +

a(n)=ceil(n*γ)
γ EulerGamma=0.5772... (Euler Gamma)
n≥0
4 operations
Arithmetic
a(n)=ceil(n/sqrt(3))
n≥0
5 operations
Power

Sequence rgefmh5czlesf

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

integer, monotonic, +

a(n)=ceil(n/ϕ)
ϕ GoldenRatio=1.618... (Golden Ratio)
n≥0
4 operations
Arithmetic

Sequence lghbrgfj4vuwf

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

integer, monotonic, +, A322042

a(n)=ceil(n*TwinPrime)
TwinPrime=0.6601... (Twin Prime)
n≥0
4 operations
Arithmetic
a(n)=∑[xor(a(n-1), a(n-2))]
a(0)=0
a(1)=1
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=∑[a(n-3)^a(n-1)]
a(0)=0
a(1)=1
a(2)=1
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=∑[C(a(n-3), a(n-1))]
a(0)=0
a(1)=1
a(2)=1
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=∑[and(1, stern(n))]
stern(n)=Stern-Brocot sequence
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence r5ynhi50ifeqo

0, 2, 3, 4, 6, 7, 8, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 24, 26, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 40, 42, 43, 44, 46, 47, 48, 50, 51, 52, 54, 55, 56, 58, 59, 60, 62, 63, 64, 66, more...

integer, strictly-monotonic, +, A004772

a(n)=ceil(n*B3)
B3=1.3325... (Mertens B3)
n≥0
4 operations
Arithmetic
a(n)=ceil(n/sqrt(W1))
W1=0.5671... (Lambert W)
n≥0
5 operations
Power
a(n)=floor(n+a(n-1)/4)
a(0)=0
n≥1
6 operations
Recursive
a(n)=a(n-1)+(n%3)!
a(0)=0
n≥1
6 operations
Combinatoric
a(n)=ceil(∑[root(7, 6+a(n-1))])
a(0)=0
root(n,a)=the n-th root of a
∑(a)=partial sums of a
n≥0
7 operations
Recursive

Sequence v53wtdx2ndwtl

0, 2, 4, 5, 7, 9, 10, 12, 13, 15, 17, 18, 20, 22, 23, 25, 26, 28, 30, 31, 33, 34, 36, 38, 39, 41, 43, 44, 46, 47, 49, 51, 52, 54, 56, 57, 59, 60, 62, 64, 65, 67, 68, 70, 72, 73, 75, 77, 78, 80, more...

integer, strictly-monotonic, +, A004956

a(n)=ceil(n*ϕ)
ϕ GoldenRatio=1.618... (Golden Ratio)
n≥0
4 operations
Arithmetic
a(n)=ceil((n+a(n-1))/ϕ)
a(0)=0
ϕ GoldenRatio=1.618... (Golden Ratio)
n≥1
6 operations
Recursive

Sequence fv4fxxagnm0bb

0, 2, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 20, 22, 24, 25, 27, 29, 30, 32, 34, 35, 37, 39, 40, 42, 44, 45, 47, 49, 50, 52, 54, 55, 57, 59, 60, 62, 64, 65, 67, 69, 70, 72, 74, 75, 77, 79, 80, 82, more...

integer, strictly-monotonic, +, A047212

a(n)=ceil(n*QR)
QR=1.6616... (Quadratic Recurrence)
n≥0
4 operations
Arithmetic
a(n)=ceil(n*root(e, 4))
e=2.7182... (Euler e)
root(n,a)=the n-th root of a
n≥0
6 operations
Power
a(n)=n+∑[xor(a(n-1), a(n-2))]
a(0)=0
a(1)=1
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=n+∑[a(n-3)^a(n-1)]
a(0)=0
a(1)=1
a(2)=1
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=n+∑[C(a(n-3), a(n-1))]
a(0)=0
a(1)=1
a(2)=1
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
6 operations
Combinatoric

Sequence 5imyotyfyznin

0, 2, 4, 6, 7, 9, 11, 13, 14, 16, 18, 20, 21, 23, 25, 26, 28, 30, 32, 33, 35, 37, 39, 40, 42, 44, 46, 47, 49, 51, 52, 54, 56, 58, 59, 61, 63, 65, 66, 68, 70, 72, 73, 75, 77, 78, 80, 82, 84, 85, more...

integer, strictly-monotonic, +, A198081

a(n)=ceil(n/γ)
γ EulerGamma=0.5772... (Euler Gamma)
n≥0
4 operations
Arithmetic
a(n)=ceil(n*sqrt(3))
n≥0
5 operations
Power

Sequence yhmiarfq0hj3d

0, 2, 4, 6, 8, 9, 11, 13, 15, 16, 18, 20, 22, 23, 25, 27, 29, 30, 32, 34, 36, 38, 39, 41, 43, 45, 46, 48, 50, 52, 53, 55, 57, 59, 60, 62, 64, 66, 68, 69, 71, 73, 75, 76, 78, 80, 82, 83, 85, 87, more...

integer, strictly-monotonic, +, A195173

a(n)=ceil(n/W1)
W1=0.5671... (Lambert W)
n≥0
4 operations
Arithmetic
a(n)=ceil(n*exp(W1))
W1=0.5671... (Lambert W)
n≥0
5 operations
Power

Sequence dpufkkp00r5td

0, 3, 6, 9, 11, 14, 17, 20, 22, 25, 28, 30, 33, 36, 39, 41, 44, 47, 49, 52, 55, 58, 60, 63, 66, 68, 71, 74, 77, 79, 82, 85, 87, 90, 93, 96, 98, 101, 104, 107, 109, 112, 115, 117, 120, 123, 126, 128, 131, 134, more...

integer, strictly-monotonic, +, A121384

a(n)=ceil(n*e)
e=2.7182... (Euler e)
n≥0
4 operations
Arithmetic
a(n)=ceil(n/exp(-1))
n≥0
6 operations
Power

Sequence krmzcemvu2kxh

0, 4, 7, 10, 13, 16, 19, 22, 26, 29, 32, 35, 38, 41, 44, 48, 51, 54, 57, 60, 63, 66, 70, 73, 76, 79, 82, 85, 88, 92, 95, 98, 101, 104, 107, 110, 114, 117, 120, 123, 126, 129, 132, 136, 139, 142, 145, 148, 151, 154, more...

integer, strictly-monotonic, +, A121381

a(n)=ceil(n*π)
π Pi=3.1415... (Pi)
n≥0
4 operations
Arithmetic

Sequence nxo1pb3dv41fc

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, more...

integer, monotonic, +, A296357

a(n)=ceil(n/π)
π Pi=3.1415... (Pi)
n≥1
4 operations
Arithmetic
a(n)=ceil(n/log(23))
n≥1
5 operations
Power

Sequence sfgg0foaf2k1k

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

integer, monotonic, +, A194979

a(n)=ceil(n*γ)
γ EulerGamma=0.5772... (Euler Gamma)
n≥1
4 operations
Arithmetic
a(n)=ceil(n/sqrt(3))
n≥1
5 operations
Power

Sequence xdjhmawoiikze

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

integer, monotonic, +, A019446

a(n)=ceil(n/ϕ)
ϕ GoldenRatio=1.618... (Golden Ratio)
n≥1
4 operations
Arithmetic
a(n)=floor(n-a(n-1)/ϕ)
a(0)=1
ϕ GoldenRatio=1.618... (Golden Ratio)
n≥2
6 operations
Recursive
a(n)=ceil(n/2^log(2))
n≥1
7 operations
Power

Sequence rwgdmqhax0pjd

2, 4, 6, 7, 9, 11, 13, 14, 16, 18, 20, 21, 23, 25, 26, 28, 30, 32, 33, 35, 37, 39, 40, 42, 44, 46, 47, 49, 51, 52, 54, 56, 58, 59, 61, 63, 65, 66, 68, 70, 72, 73, 75, 77, 78, 80, 82, 84, 85, 87, more...

integer, strictly-monotonic, +, A081223

a(n)=ceil(n/γ)
γ EulerGamma=0.5772... (Euler Gamma)
n≥1
4 operations
Arithmetic
a(n)=ceil(n*sqrt(3))
n≥1
5 operations
Power

Sequence xaqtussto12te

-10, -5, -3, -2, -2, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, monotonic, -

a(n)=ceil(-10/n)
n≥1
5 operations
Arithmetic

Sequence 40evnabu2pkbk

-9, -4, -3, -2, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, monotonic, -

a(n)=ceil(-9/n)
n≥1
5 operations
Arithmetic

Sequence nx0fyioc0od4j

-8, -4, -2, -2, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, monotonic, -

a(n)=ceil(-8/n)
n≥1
5 operations
Arithmetic

Sequence dk12pai0cyo1b

-7, -3, -2, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, monotonic, -

a(n)=ceil(-7/n)
n≥1
5 operations
Arithmetic

Sequence zrecsrymgo2od

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

integer, monotonic, -

a(n)=ceil(-6/n)
n≥1
5 operations
Arithmetic

Sequence rzxtdkbmggqxi

0, 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, more...

integer, monotonic, -

a(n)=ceil(-n/2)
n≥0
5 operations
Arithmetic
a(n)=1-n-a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=-∑[a(n-2)^a(n-1)]
a(0)=0
a(1)=0
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=-∑[C(a(n-2), a(n-1))]
a(0)=0
a(1)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑[and(1, n)]-n
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
6 operations
Bitwise

Sequence rw2xcl4ktnyid

0, 0, 0, -1, -1, -1, -2, -2, -2, -3, -3, -3, -4, -4, -4, -5, -5, -5, -6, -6, -6, -7, -7, -7, -8, -8, -8, -9, -9, -9, -10, -10, -10, -11, -11, -11, -12, -12, -12, -13, -13, -13, -14, -14, -14, -15, -15, -15, -16, -16, more...

integer, monotonic, -

a(n)=ceil(-n/3)
n≥0
5 operations
Arithmetic
a(n)=∑[xor(a(n-1), a(n-2))]-n
a(0)=0
a(1)=1
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=floor(log(2)-n/3)
n≥0
7 operations
Power

Sequence 4d1fndmlbprvc

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

integer, monotonic, -

a(n)=ceil(-n/4)
n≥0
5 operations
Arithmetic

Sequence cokdrjsooa50b

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

integer, monotonic, -

a(n)=ceil(-n/5)
n≥0
5 operations
Arithmetic

Sequence ejegpt3kjfofk

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

integer, monotonic, -

a(n)=ceil(-n/6)
n≥0
5 operations
Arithmetic

Sequence zy5krfalbf2jd

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

integer, monotonic, -

a(n)=ceil(-n/7)
n≥0
5 operations
Arithmetic

Sequence bgb01ibjiq2ri

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

integer, monotonic, -

a(n)=ceil(-n/8)
n≥0
5 operations
Arithmetic

Sequence 1zmieay4v2bhc

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

integer, monotonic, -

a(n)=ceil(-n/9)
n≥0
5 operations
Arithmetic

Sequence ustpxcij0w2lf

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

integer, monotonic, -

a(n)=ceil(-n/10)
n≥0
5 operations
Arithmetic

Sequence riav3p5aod32c

0, 0.5, 0.5, 1, 1, 1.5, 1.5, 2, 2, 2.5, 2.5, 3, 3, 3.5, 3.5, 4, 4, 4.5, 4.5, 5, 5, 5.5, 5.5, 6, 6, more...

decimal, monotonic, +

a(n)=n/2-a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=ceil(n/2)/2
n≥0
6 operations
Arithmetic
a(n)=∑[and(1, n)/2]
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
6 operations
Bitwise
a(n)=floor(n/2)%n/2
n≥1
8 operations
Divisibility

Sequence qghtubzezhvbh

0, 3, 6, 8, 11, 14, 16, 19, 22, 24, 27, 30, 32, 35, 38, 40, 43, 46, 48, 51, 54, 56, 59, 62, 64, 67, 70, 72, 75, 78, 80, 83, 86, 88, 91, 94, 96, 99, 102, 104, 107, 110, 112, 115, 118, 120, 123, 126, 128, 131, more...

integer, strictly-monotonic, +, A047399

a(n)=ceil(n/log(Backhouse))
Backhouse=1.456... (Backhouse)
n≥0
5 operations
Power
a(n)=ceil(8*n/3)
n≥0
6 operations
Arithmetic
a(n)=round(∑[log2(9-a(n-1))])
a(0)=0
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=round(∑[3-a(n-1)/8])
a(0)=0
∑(a)=partial sums of a
n≥0
7 operations
Recursive
a(n)=∑[gpf(6/gcd(n, a(n-1)))]
a(0)=0
gcd(a,b)=greatest common divisor
gpf(n)=greatest prime factor of n
∑(a)=partial sums of a
n≥0
7 operations
Prime

Sequence bs0uewotmm2eh

0, 4, 7, 11, 14, 18, 21, 25, 28, 32, 35, 39, 42, 46, 49, 53, 56, 60, 63, 67, 70, 74, 77, 81, 84, 88, 91, 95, 98, 102, 105, 109, 112, 116, 119, 123, 126, 130, 133, 137, 140, 144, 147, 151, 154, 158, 161, 165, 168, 172, more...

integer, strictly-monotonic, +, A047345

a(n)=ceil(n*log(33))
n≥0
5 operations
Power
a(n)=∑[stern(18-a(n-1))]
a(0)=0
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[5-pt(a(n-1))]
a(0)=0
pt(n)=Pascals triangle by rows
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑[agc(or(35, a(n-1)))]
a(0)=0
or(a,b)=bitwise or
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
5 operations
Prime
a(n)=ceil(7*n/2)
n≥0
6 operations
Arithmetic

Sequence ganeoy0ig4iye

1, 1, 0, 0, 0, -1, -1, -1, -2, -2, -2, -3, -3, -3, -4, -4, -4, -5, -5, -5, -6, -6, -6, -7, -7, -7, -8, -8, -8, -9, -9, -9, -10, -10, -10, -11, -11, -11, -12, -12, -12, -13, -13, -13, -14, -14, -14, -15, -15, -15, more...

integer, monotonic, +-

a(n)=∑[-C(a(n-2), a(n-1))]
a(0)=1
a(1)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=ceil((2-n)/3)
n≥0
6 operations
Arithmetic
a(n)=a(n-1)-char[3+a(n-1)]
a(0)=1
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive
a(n)=∑[xor(a(n-1), a(n-2))]-n
a(0)=1
a(1)=1
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=floor(sqrt(2)-n/3)
n≥0
7 operations
Power

Sequence mnbx2njoc3kfp

1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, more...

integer, monotonic, +

a(n)=∑[C(-a(n-1), a(n-2))]
a(0)=1
a(1)=1
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=stern(ω(a(n-1)))+a(n-3)
a(0)=1
a(1)=2
a(2)=2
ω(n)=number of distinct prime divisors of n
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Prime
a(n)=a(n-3)+pt(agc(a(n-1)))
a(0)=1
a(1)=2
a(2)=2
agc(n)=number of factorizations into prime powers (abelian group count)
pt(n)=Pascals triangle by rows
n≥0
5 operations
Prime
a(n)=ceil(1+n/3)
n≥0
6 operations
Arithmetic
a(n)=char[3*n]+a(n-1)
a(0)=1
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive

Sequence ibd33otwz5aoh

2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, more...

integer, monotonic, +

a(n)=∑[C(-a(n-1), a(n-2))]
a(0)=2
a(1)=1
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=ceil(2+n/3)
n≥0
6 operations
Arithmetic
a(n)=char[3*n]+a(n-1)
a(0)=2
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive

Sequence 0t4b0jkzm53sd

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, 25, 26, 26, 27, 27, 28, more...

integer, monotonic, +

a(n)=6+n-a(n-1)
a(0)=3
n≥0
5 operations
Recursive
a(n)=∑[stern(xor(1, a(n-1)))]
a(0)=3
xor(a,b)=bitwise exclusive or
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[and(n, P(a(n-1)))]
a(0)=3
P(n)=partition numbers
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑[xor(a(n-1), agc(a(n-1)))]
a(0)=3
agc(n)=number of factorizations into prime powers (abelian group count)
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥0
5 operations
Prime
a(n)=ceil(3+n/2)
n≥0
6 operations
Arithmetic

Sequence lfeymrzmk4aej

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

integer, monotonic, +, A171623

a(n)=round(4/sqrt(n))
n≥1
5 operations
Power
a(n)=τ(ceil(8/n))
τ(n)=number of divisors of n
n≥1
5 operations
Prime
a(n)=ceil(43/zetazero(n))
zetazero(n)=non trivial zeros of Riemann zeta
n≥0
5 operations
Prime
a(n)=ceil(15/composite(n))
composite(n)=nth composite number
n≥2
5 operations
Prime
a(n)=ceil(10/(1+n))
n≥2
6 operations
Arithmetic

Sequence vvgqln2tom01i

-3, -2, -2, -2, -1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, more...

integer, monotonic, +-

a(n)=ceil(n/3-3)
n≥0
6 operations
Arithmetic

Sequence g3gaytyjvkwto

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

integer, monotonic, +-

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

Sequence nljhma0wczkvc

-2, -1, -1, -1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, more...

integer, monotonic, +-

a(n)=ceil(n/3-2)
n≥0
6 operations
Arithmetic
a(n)=floor(n/3-log(3))
n≥0
7 operations
Power

Sequence dcwsawyzjzxpd

0, 0.3333333333333333, 0.3333333333333333, 0.3333333333333333, 0.6666666666666666, 0.6666666666666666, 0.6666666666666666, 1, 1, 1, 1.3333333333333333, 1.3333333333333333, 1.3333333333333333, 1.6666666666666667, 1.6666666666666667, 1.6666666666666667, 2, 2, 2, 2.3333333333333335, 2.3333333333333335, 2.3333333333333335, 2.6666666666666665, 2.6666666666666665, 2.6666666666666665, more...

decimal, monotonic, +

a(n)=ceil(n/3)/3
n≥0
6 operations
Arithmetic

Sequence atwrzj2nf2ukh

0, 0.3333333333333333, 0.3333333333333333, 0.6666666666666666, 0.6666666666666666, 1, 1, 1.3333333333333333, 1.3333333333333333, 1.6666666666666667, 1.6666666666666667, 2, 2, 2.3333333333333335, 2.3333333333333335, 2.6666666666666665, 2.6666666666666665, 3, 3, 3.3333333333333335, 3.3333333333333335, 3.6666666666666665, 3.6666666666666665, 4, 4, more...

decimal, monotonic, +

a(n)=ceil(n/2)/3
n≥0
6 operations
Arithmetic
a(n)=∑[1-a(n-1)]/3
a(0)=0
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence 3lh1xnl1nsby

0, 0.5, 0.5, 0.5, 1, 1, 1, 1.5, 1.5, 1.5, 2, 2, 2, 2.5, 2.5, 2.5, 3, 3, 3, 3.5, 3.5, 3.5, 4, 4, 4, more...

decimal, monotonic, +

a(n)=ceil(n/3)/2
n≥0
6 operations
Arithmetic

Sequence mzbbrbqybibfg

0, 2, 2, 2, 4, 4, 4, 6, 6, 6, 8, 8, 8, 10, 10, 10, 12, 12, 12, 14, 14, 14, 16, 16, 16, 18, 18, 18, 20, 20, 20, 22, 22, 22, 24, 24, 24, 26, 26, 26, 28, 28, 28, 30, 30, 30, 32, 32, 32, 34, more...

integer, monotonic, +, A302402

a(n)=2*ceil(n/3)
n≥0
6 operations
Arithmetic
a(n)=∑[gcd(n, 3)-1]
gcd(a,b)=greatest common divisor
∑(a)=partial sums of a
n≥2
6 operations
Divisibility
a(n)=∑[Ω(gcd(n, 3)²)]
gcd(a,b)=greatest common divisor
Ω(n)=number of prime divisors of n
∑(a)=partial sums of a
n≥2
6 operations
Prime
a(n)=∑[ω(gcd(n, 3)!)]
gcd(a,b)=greatest common divisor
ω(n)=number of distinct prime divisors of n
∑(a)=partial sums of a
n≥2
6 operations
Prime
a(n)=gcd(n, 3)-1+a(n-1)
a(0)=0
gcd(a,b)=greatest common divisor
n≥2
7 operations
Recursive

Sequence w1niun1bowjip

0, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, more...

integer, strictly-monotonic, +, A047594

a(n)=ceil(8*n/7)
n≥0
6 operations
Arithmetic
a(n)=floor(n+a(n-1)/8)
a(0)=0
n≥1
6 operations
Recursive

Sequence naccocxyjx2mp

0, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 58, more...

integer, strictly-monotonic, +, A047306

a(n)=ceil(7*n/6)
n≥0
6 operations
Arithmetic
a(n)=ceil(n*root(9, 4))
root(n,a)=the n-th root of a
n≥0
6 operations
Power
a(n)=floor(n+a(n-1)/7)
a(0)=0
n≥1
6 operations
Recursive

Sequence nq1b0nv1gdgtl

0, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 56, 57, 58, 59, more...

integer, strictly-monotonic, +, A047248

a(n)=ceil(6*n/5)
n≥0
6 operations
Arithmetic
a(n)=ceil(n*root(9, 5))
root(n,a)=the n-th root of a
n≥0
6 operations
Power
a(n)=floor(n+a(n-1)/6)
a(0)=0
n≥1
6 operations
Recursive

Sequence 2aulmy04mitgc

0, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 62, more...

integer, strictly-monotonic, +, A047203

a(n)=ceil(5*n/4)
n≥0
6 operations
Arithmetic
a(n)=ceil(n*root(5, 3))
root(n,a)=the n-th root of a
n≥0
6 operations
Power
a(n)=floor(n+a(n-1)/5)
a(0)=0
n≥1
6 operations
Recursive
a(n)=a(n-1)+agc(and(3, n))
a(0)=0
and(a,b)=bitwise and
agc(n)=number of factorizations into prime powers (abelian group count)
n≥2
6 operations
Prime
a(n)=∑[P(and(n, 3-a(n-1)))]
a(0)=0
and(a,b)=bitwise and
P(n)=partition numbers
∑(a)=partial sums of a
n≥1
7 operations
Combinatoric

Sequence aspqqqmncjp4e

0, 2, 3, 5, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 21, 23, 24, 26, 27, 28, 30, 31, 33, 34, 35, 37, 38, 40, 41, 42, 44, 45, 47, 48, 49, 51, 52, 54, 55, 56, 58, 59, 61, 62, 63, 65, 66, 68, 69, more...

integer, strictly-monotonic, +, A047332

a(n)=ceil(7*n/5)
n≥0
6 operations
Arithmetic
a(n)=ceil(∑[root(5, 4+a(n-1))])
a(0)=0
root(n,a)=the n-th root of a
∑(a)=partial sums of a
n≥0
7 operations
Recursive
a(n)=n+∑[char[∑[Ω(52-a(n-1))]]]
a(0)=1
Ω(n)=number of prime divisors of n
∑(a)=partial sums of a
char(a)=characteristic function of a (in range)
n≥0
9 operations
Prime

Sequence znu2dalzemsie

0, 2, 4, 5, 7, 8, 10, 12, 13, 15, 16, 18, 20, 21, 23, 24, 26, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 44, 45, 47, 48, 50, 52, 53, 55, 56, 58, 60, 61, 63, 64, 66, 68, 69, 71, 72, 74, 76, 77, 79, more...

integer, strictly-monotonic, +, A047496

a(n)=ceil(8*n/5)
n≥0
6 operations
Arithmetic
a(n)=round(∑[2-a(n-1)/4])
a(0)=0
∑(a)=partial sums of a
n≥0
7 operations
Recursive
a(n)=floor(Δ[(2*n)²]/5)
Δ(a)=differences of a
n≥0
8 operations
Power

Sequence qtcmtxozcolgi

0, 2, 4, 6, 7, 9, 11, 13, 14, 16, 18, 20, 21, 23, 25, 27, 28, 30, 32, 34, 35, 37, 39, 41, 42, 44, 46, 48, 49, 51, 53, 55, 56, 58, 60, 62, 63, 65, 67, 69, 70, 72, 74, 76, 77, 79, 81, 83, 84, 86, more...

integer, strictly-monotonic, +, A047293

a(n)=ceil(7*n/4)
n≥0
6 operations
Arithmetic
a(n)=ceil(n/log(sqrt(π)))
π Pi=3.1415... (Pi)
n≥0
6 operations
Power
a(n)=round(∑[(7-a(n-1))/3])
a(0)=0
∑(a)=partial sums of a
n≥0
7 operations
Recursive
a(n)=∑[catalan(and(2, n-a(n-1)))]
a(0)=0
and(a,b)=bitwise and
catalan(n)=the catalan numbers
∑(a)=partial sums of a
n≥2
7 operations
Combinatoric
a(n)=∑[P(and(2, n-a(n-1)))]
a(0)=0
and(a,b)=bitwise and
P(n)=partition numbers
∑(a)=partial sums of a
n≥2
7 operations
Combinatoric

Sequence yswub3vcjzqen

0, 3, 3, 3, 6, 6, 6, 9, 9, 9, 12, 12, 12, 15, 15, 15, 18, 18, 18, 21, 21, 21, 24, 24, 24, 27, 27, 27, 30, 30, 30, 33, 33, 33, 36, 36, 36, 39, 39, 39, 42, 42, 42, 45, 45, 45, 48, 48, 48, 51, more...

integer, monotonic, +

a(n)=3*ceil(n/3)
n≥0
6 operations
Arithmetic

Sequence jxawbvunldy2j

0, 3, 5, 7, 10, 12, 14, 17, 19, 21, 24, 26, 28, 31, 33, 35, 38, 40, 42, 45, 47, 49, 52, 54, 56, 59, 61, 63, 66, 68, 70, 73, 75, 77, 80, 82, 84, 87, 89, 91, 94, 96, 98, 101, 103, 105, 108, 110, 112, 115, more...

integer, strictly-monotonic, +, A047390

a(n)=ceil(7*n/3)
n≥0
6 operations
Arithmetic
a(n)=ceil(n*root(e, 10))
e=2.7182... (Euler e)
root(n,a)=the n-th root of a
n≥0
6 operations
Power
a(n)=ceil(∑[log(8+a(n-1))])
a(0)=0
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=floor(∑[(7-a(n-1))/2])
a(0)=0
∑(a)=partial sums of a
n≥0
7 operations
Recursive
a(n)=floor(∑[8-ω(a(n-1))]/3)
a(0)=1
ω(n)=number of distinct prime divisors of n
∑(a)=partial sums of a
n≥0
8 operations
Prime

Sequence l21o0wp1catxg

1, 1, 1, 0.5, 0.5, 0.5, 0.3333333333333333, 0.3333333333333333, 0.3333333333333333, 0.25, 0.25, 0.25, 0.2, 0.2, 0.2, 0.16666666666666666, 0.16666666666666666, 0.16666666666666666, 0.14285714285714285, 0.14285714285714285, 0.14285714285714285, 0.125, 0.125, 0.125, 0.1111111111111111, more...

decimal, monotonic, +

a(n)=1/ceil(n/3)
n≥1
6 operations
Arithmetic

Sequence 24lrkh12cqgel

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

integer, monotonic, +, A225875

a(n)=ceil(4/(7/n))
n≥1
6 operations
Arithmetic
a(n)=ceil(n-n/log2(5))
n≥1
7 operations
Power
a(n)=round(∑[(4+a(n-1))/8])
a(0)=1
∑(a)=partial sums of a
n≥0
7 operations
Recursive
a(n)=∑[C(char[7*n], a(n-1))]
a(0)=1
char(a)=characteristic function of a (in range)
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
7 operations
Combinatoric
a(n)=∑[Ω(Ω(9-n%7))]
Ω(n)=number of prime divisors of n
∑(a)=partial sums of a
n≥0
8 operations
Prime

Sequence dhs3p323zgdli

2, 2, 2, 1, 1, 1, 0.6666666666666666, 0.6666666666666666, 0.6666666666666666, 0.5, 0.5, 0.5, 0.4, 0.4, 0.4, 0.3333333333333333, 0.3333333333333333, 0.3333333333333333, 0.2857142857142857, 0.2857142857142857, 0.2857142857142857, 0.25, 0.25, 0.25, 0.2222222222222222, more...

decimal, monotonic, +

a(n)=2/ceil(n/3)
n≥1
6 operations
Arithmetic

Sequence mim0lbaszptzj

2, 2, 4, 4, 4, 6, 6, 6, 8, 8, 8, 10, 10, 10, 12, 12, 12, 14, 14, 14, 16, 16, 16, 18, 18, 18, 20, 20, 20, 22, 22, 22, 24, 24, 24, 26, 26, 26, 28, 28, 28, 30, 30, 30, 32, 32, 32, 34, 34, 34, more...

integer, monotonic, +, A110870 (weak, multiple)

a(n)=2*ceil(n/3)
n≥2
6 operations
Arithmetic
a(n)=2-∑[1-gcd(n, 3)]
gcd(a,b)=greatest common divisor
∑(a)=partial sums of a
n≥1
8 operations
Divisibility
a(n)=Δ[floor((n+n²)/3)]
Δ(a)=differences of a
n≥2
8 operations
Power
a(n)=2*∑[n%gcd(a(n-1), 3)]
a(0)=1
gcd(a,b)=greatest common divisor
∑(a)=partial sums of a
n≥2
8 operations
Recursive
a(n)=n-∑[and(2, a(n-2))-a(n-1)]
a(0)=0
a(1)=1
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥2
8 operations
Recursive

Sequence tyl5hkgqqu1wh

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 99, 100, more...

integer, strictly-monotonic, +

a(n)=ceil(2/(1/n))
n≥1
6 operations
Arithmetic

Sequence zhax11mabceol

3, 3, 3, 1.5, 1.5, 1.5, 1, 1, 1, 0.75, 0.75, 0.75, 0.6, 0.6, 0.6, 0.5, 0.5, 0.5, 0.42857142857142855, 0.42857142857142855, 0.42857142857142855, 0.375, 0.375, 0.375, 0.3333333333333333, more...

decimal, monotonic, +

a(n)=3/ceil(n/3)
n≥1
6 operations
Arithmetic

Sequence qzc1jripa4cbi

3, 3, 6, 6, 6, 9, 9, 9, 12, 12, 12, 15, 15, 15, 18, 18, 18, 21, 21, 21, 24, 24, 24, 27, 27, 27, 30, 30, 30, 33, 33, 33, 36, 36, 36, 39, 39, 39, 42, 42, 42, 45, 45, 45, 48, 48, 48, 51, 51, 51, more...

integer, monotonic, +, A105676 (multiple)

a(n)=3*ceil(n/3)
n≥2
6 operations
Arithmetic
a(n)=3-(n%3-n)
n≥1
7 operations
Divisibility
a(n)=n+P(3-n%3)
P(n)=partition numbers
n≥1
8 operations
Combinatoric
a(n)=n+gpf(3-n%3)
gpf(n)=greatest prime factor of n
n≥1
8 operations
Prime
a(n)=n+rad(3-n%3)
rad(n)=square free kernel of n
n≥1
8 operations
Prime

Sequence m1vvlu4isoq4f

3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, more...

integer, monotonic, +

a(n)=ceil(3+n/3)
n≥0
6 operations
Arithmetic

Sequence woas3og2hkgej

4, 4, 8, 8, 8, 12, 12, 12, 16, 16, 16, 20, 20, 20, 24, 24, 24, 28, 28, 28, 32, 32, 32, 36, 36, 36, 40, 40, 40, 44, 44, 44, 48, 48, 48, 52, 52, 52, 56, 56, 56, 60, 60, 60, 64, 64, 64, 68, 68, 68, more...

integer, monotonic, +, A105675 (weak, multiple)

a(n)=4*ceil(n/3)
n≥2
6 operations
Arithmetic
a(n)=4*∑[n%gcd(a(n-1), 3)]
a(0)=1
gcd(a,b)=greatest common divisor
∑(a)=partial sums of a
n≥2
8 operations
Recursive

Sequence 5w5ni5wonk1uf

6, 6, 6, 12, 12, 12, 18, 18, 18, 24, 24, 24, 30, 30, 30, 36, 36, 36, 42, 42, 42, 48, 48, 48, 54, 54, 54, 60, 60, 60, 66, 66, 66, 72, 72, 72, 78, 78, 78, 84, 84, 84, 90, 90, 90, 96, 96, 96, 102, 102, more...

integer, monotonic, +, A052380

a(n)=6*ceil(n/3)
n≥1
6 operations
Arithmetic
a(n)=∑[6*∑[n]%3]
∑(a)=partial sums of a
n≥1
7 operations
Divisibility
a(n)=∑[6*char[3+a(n-1)]]
a(0)=0
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
7 operations
Recursive
a(n)=∑[and(6, gcd(n, 3)!)]
gcd(a,b)=greatest common divisor
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
7 operations
Combinatoric
a(n)=∑[Ω(gcd(n, 3)^6)]
gcd(a,b)=greatest common divisor
Ω(n)=number of prime divisors of n
∑(a)=partial sums of a
n≥0
7 operations
Prime

Sequence r4qnlifhhzngi

8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 197, 200, 204, more...

integer, strictly-monotonic, +, A192544 (multiple)

a(n)=ceil(4/(1/n))
n≥2
6 operations
Arithmetic
a(n)=ceil(4/root(-1, n))
root(n,a)=the n-th root of a
n≥2
7 operations
Power

Sequence 34ntxxwen5hup

0, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 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, monotonic, +, A004233

a(n)=ceil(log(n))
n≥1
3 operations
Power
a(n)=ceil(log(n)/ζ(7))
ζ(n)=Riemann zeta
n≥1
6 operations
Prime
a(n)=Δ[ceil(log(n)+a(n-1))]
a(0)=1
Δ(a)=differences of a
n≥0
6 operations
Recursive
a(n)=∑[char[floor(exp(stern(n)))]]
stern(n)=Stern-Brocot sequence
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=ceil(root(ζ(7), log(n)))
ζ(n)=Riemann zeta
root(n,a)=the n-th root of a
n≥1
6 operations
Prime

Sequence gwyogtngbtfxf

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

integer, monotonic, +, A135034

a(n)=ceil(sqrt(n))
n≥0
3 operations
Power
a(n)=char[n²]+a(n-1)
a(0)=0
char(a)=characteristic function of a (in range)
n≥0
5 operations
Recursive
a(n)=ceil(sqrt(n)/ζ(7))
ζ(n)=Riemann zeta
n≥0
6 operations
Prime
a(n)=ceil(root(ζ(8), sqrt(n)))
ζ(n)=Riemann zeta
root(n,a)=the n-th root of a
n≥0
6 operations
Prime
a(n)=and(7, char[n²]+a(n-1))
a(0)=0
char(a)=characteristic function of a (in range)
and(a,b)=bitwise and
n≥0
7 operations
Recursive

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