Sequence Database

A database with 2076264 machine generated integer and decimal sequences.

Displaying result 0-99 of total 23452. [0] [1] [2] [3] [4] ... [234]

Sequence jtrnud52ggzpi

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

integer, monotonic, +, A297045

a(n)=floor(tanh(n))
n≥1
3 operations
Trigonometric
a(n)=round(n/37)
n≥0
4 operations
Arithmetic
a(n)=floor(log(n)/3)
n≥2
5 operations
Power
a(n)=round(n/zetazero(5))
zetazero(n)=non trivial zeros of Riemann zeta
n≥0
5 operations
Prime
a(n)=a(n-1)^∑[9-n]
a(0)=0
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence 42a4hlvqdc04d

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

integer, monotonic, +, A023974

a(n)=round(n/33)
n≥0
4 operations
Arithmetic
a(n)=floor(sqrt(n/17))
n≥0
5 operations
Power
a(n)=stern(floor(n/17))
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Recursive
a(n)=a(n-1)^(17-n)
a(0)=0
n≥0
5 operations
Recursive
a(n)=round(n/zetazero(4))
zetazero(n)=non trivial zeros of Riemann zeta
n≥0
5 operations
Prime

Sequence iqh4zaekqjw0o

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

integer, monotonic, +, A194698

a(n)=round(n/24)
n≥0
4 operations
Arithmetic
a(n)=floor(zetazero(n)/58)
zetazero(n)=non trivial zeros of Riemann zeta
n≥0
5 operations
Prime
a(n)=round(n/exp(log2(9)))
n≥0
6 operations
Power
a(n)=round(∑[5^(a(n-1)-2)])
a(0)=0
∑(a)=partial sums of a
n≥0
7 operations
Recursive
a(n)=floor(∑[Ω(ω(∑[n]))/n])
∑(a)=partial sums of a
ω(n)=number of distinct prime divisors of n
Ω(n)=number of prime divisors of n
n≥2
8 operations
Prime

Sequence d44dqiub0qpbp

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

integer, monotonic, +

a(n)=round(n/10)
n≥0
4 operations
Arithmetic
a(n)=round(n/π²)
π Pi=3.1415... (Pi)
n≥0
5 operations
Power
a(n)=∑[char[10+a(n-1)]]
a(0)=5
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence yni4trkbjukzb

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

integer, monotonic, +

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

Sequence yfxnattjvuekd

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

integer, monotonic, +, A071701

a(n)=round(n/12)
n≥2
4 operations
Arithmetic
a(n)=∑[char[12+a(n-1)]]
a(0)=4
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=round(n/4^log(6))
n≥2
7 operations
Power
a(n)=round(n/composite(or(7, a(n-1))))
a(0)=0
or(a,b)=bitwise or
composite(n)=nth composite number
n≥2
7 operations
Prime
a(n)=round(xor(1, n)/3/4)
xor(a,b)=bitwise exclusive or
n≥2
8 operations
Bitwise

Sequence caux0k0pjc1qi

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, 6, 6, 6, 6, more...

integer, monotonic, +

a(n)=round(n/8)
n≥0
4 operations
Arithmetic
a(n)=∑[char[8+a(n-1)]]
a(0)=4
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence rkhl4anzbvfyg

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, 7, 7, 7, more...

integer, monotonic, +

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

Sequence h0c2ihfmtkl5

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, 8, 8, 8, more...

integer, monotonic, +

a(n)=round(n/6)
n≥0
4 operations
Arithmetic
a(n)=∑[char[6+a(n-1)]]
a(0)=3
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence yuimginadyryi

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, 10, 10, more...

integer, monotonic, +

a(n)=round(n/5)
n≥0
4 operations
Arithmetic
a(n)=round(n/exp(ϕ))
ϕ GoldenRatio=1.618... (Golden Ratio)
n≥0
5 operations
Power
a(n)=∑[char[5+a(n-1)]]
a(0)=3
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence 1irmtzlkgc0de

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, 12, 12, more...

integer, monotonic, +

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

Sequence id4o55c2nmbkg

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, 16, more...

integer, monotonic, +

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

Sequence fmfwfatghy3cm

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, 0, more...

integer, monotonic, +

a(n)=round(3/n)
n≥1
4 operations
Arithmetic
a(n)=round(log2(9)/n)
n≥1
5 operations
Power

Sequence wlrxkksveqcmp

4, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, monotonic, +

a(n)=round(4/n)
n≥1
4 operations
Arithmetic
a(n)=floor(3/log(p(n)))
p(n)=nth prime
n≥1
6 operations
Prime
a(n)=round(n*(2/n)²)
n≥1
7 operations
Power

Sequence yce5xosy32wwg

5, 3, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, monotonic, +

a(n)=round(5/n)
n≥1
4 operations
Arithmetic
a(n)=round(exp(ϕ)/n)
ϕ GoldenRatio=1.618... (Golden Ratio)
n≥1
5 operations
Power

Sequence nbjgutqp1mg5b

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

integer, monotonic, +

a(n)=round(6/n)
n≥1
4 operations
Arithmetic

Sequence w4vgabec1gpaj

7, 4, 2, 2, 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, 0, 0, 0, 0, 0, 0, more...

integer, monotonic, +

a(n)=round(7/n)
n≥1
4 operations
Arithmetic
a(n)=round(e²/n)
e=2.7182... (Euler e)
n≥1
5 operations
Power

Sequence qckcmtgh0pf1

8, 4, 3, 2, 2, 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, 0, 0, 0, 0, more...

integer, monotonic, +

a(n)=round(8/n)
n≥1
4 operations
Arithmetic

Sequence 133fpf5ozcjsk

9, 5, 3, 2, 2, 2, 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, 0, 0, more...

integer, monotonic, +

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

Sequence z13nvg3rlmz4o

10, 5, 3, 3, 2, 2, 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, monotonic, +

a(n)=round(10/n)
n≥1
4 operations
Arithmetic

Sequence 3dbc0n1bpbvqd

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

integer, monotonic, +

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

Sequence b43aonerv1eye

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

integer, monotonic, +

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

Sequence i35mds4cgzdje

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

integer, monotonic, +, A082964

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

Sequence vekezmh4fabvl

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

integer, monotonic, +, A225593

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

Sequence bd0lu1ruitdmi

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

integer, monotonic, +

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

Sequence 3rfrfi2kgnqeo

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

integer, monotonic, +, A101803

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

Sequence qdajgjyute32c

0, 1, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, more...

integer, strictly-monotonic, +, A042965

a(n)=round(n*B3)
B3=1.3325... (Mertens B3)
n≥0
4 operations
Arithmetic
a(n)=gcd(a(n-2), 2)+a(n-1)
a(0)=0
a(1)=1
gcd(a,b)=greatest common divisor
n≥0
5 operations
Recursive
a(n)=∑[or(log2(a(n-1)), a(n-3))]
a(0)=0
a(1)=1
a(2)=2
or(a,b)=bitwise or
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[gcd(log2(a(n-1)), a(n-3))]
a(0)=0
a(1)=1
a(2)=2
gcd(a,b)=greatest common divisor
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[root(a(n-1), a(n-3))!]
a(0)=0
a(1)=1
a(2)=2
root(n,a)=the n-th root of a
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric

Sequence ae3wfbhsdib4c

0, 2, 3, 5, 6, 8, 10, 11, 13, 15, 16, 18, 19, 21, 23, 24, 26, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 44, 45, 47, 49, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 70, 71, 73, 74, 76, 78, 79, more...

integer, strictly-monotonic, +, A007067

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

Sequence nt4ctige222ml

0, 2, 3, 5, 7, 9, 10, 12, 14, 16, 17, 19, 21, 23, 24, 26, 28, 29, 31, 33, 35, 36, 38, 40, 42, 43, 45, 47, 49, 50, 52, 54, 55, 57, 59, 61, 62, 64, 66, 68, 69, 71, 73, 74, 76, 78, 80, 81, 83, 85, more...

integer, strictly-monotonic, +

a(n)=round(n/γ)
γ EulerGamma=0.5772... (Euler Gamma)
n≥0
4 operations
Arithmetic

Sequence b2y5mc4d1ysij

0, 3, 5, 8, 11, 14, 16, 19, 22, 24, 27, 30, 33, 35, 38, 41, 43, 46, 49, 52, 54, 57, 60, 63, 65, 68, 71, 73, 76, 79, 82, 84, 87, 90, 92, 95, 98, 101, 103, 106, 109, 111, 114, 117, 120, 122, 125, 128, 130, 133, more...

integer, strictly-monotonic, +, A022852

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

Sequence g5ll4snpfqhuh

0, 3, 6, 9, 13, 16, 19, 22, 25, 28, 31, 35, 38, 41, 44, 47, 50, 53, 57, 60, 63, 66, 69, 72, 75, 79, 82, 85, 88, 91, 94, 97, 101, 104, 107, 110, 113, 116, 119, 123, 126, 129, 132, 135, 138, 141, 145, 148, 151, 154, more...

integer, strictly-monotonic, +, A022853

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

Sequence ggpghb4ggmosc

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

integer, monotonic, +, A210434

a(n)=round(n/QR)
QR=1.6616... (Quadratic Recurrence)
n≥1
4 operations
Arithmetic
a(n)=round(n/root(e, 4))
e=2.7182... (Euler e)
root(n,a)=the n-th root of a
n≥1
6 operations
Power
a(n)=gcd(stern(a(n-1)), 2)+a(n-2)
a(0)=1
a(1)=1
stern(n)=Stern-Brocot sequence
gcd(a,b)=greatest common divisor
n≥0
6 operations
Recursive
a(n)=floor(∑[(3+a(n-1))/6])
a(0)=1
∑(a)=partial sums of a
n≥0
7 operations
Recursive
a(n)=∑[1-(n%5)%2]
∑(a)=partial sums of a
n≥0
8 operations
Divisibility

Sequence odvksyzfsoebi

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

integer, monotonic, +, A066530

a(n)=round(n/B3)
B3=1.3325... (Mertens B3)
n≥1
4 operations
Arithmetic
a(n)=round(n*sqrt(W1))
W1=0.5671... (Lambert W)
n≥1
5 operations
Power
a(n)=round(n-a(n-1)/3)
a(0)=1
n≥1
6 operations
Recursive
a(n)=∑[stern(and(5, n²))]
and(a,b)=bitwise and
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥2
6 operations
Recursive
a(n)=∑[xor(and(n, a(n-1)), a(n-2))]
a(0)=1
a(1)=1
and(a,b)=bitwise and
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥1
6 operations
Recursive

Sequence x1bxklvepiung

1, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, more...

integer, strictly-monotonic, +, A122906

a(n)=round(n*B3)
B3=1.3325... (Mertens B3)
n≥1
4 operations
Arithmetic
a(n)=∑[(n%3)!]
∑(a)=partial sums of a
n≥1
5 operations
Combinatoric
a(n)=round(n*root(8, 10))
root(n,a)=the n-th root of a
n≥1
6 operations
Power
a(n)=ceil(n+a(n-1)/4)
a(0)=1
n≥1
6 operations
Recursive
a(n)=∑[2/a(n-1)/a(n-2)]
a(0)=1
a(1)=2
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence ricmmycgnk2rm

2, 3, 5, 7, 8, 10, 12, 13, 15, 17, 18, 20, 22, 23, 25, 27, 28, 30, 32, 33, 35, 37, 38, 40, 42, 43, 45, 47, 48, 50, 52, 53, 55, 56, 58, 60, 61, 63, 65, 66, 68, 70, 71, 73, 75, 76, 78, 80, 81, 83, more...

integer, strictly-monotonic, +, A028738 (multiple)

a(n)=round(n*QR)
QR=1.6616... (Quadratic Recurrence)
n≥1
4 operations
Arithmetic

Sequence so051llk23xvb

-10, -5, -3, -3, -2, -2, -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, monotonic, -

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

Sequence txrv2n5vq0k3i

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

integer, monotonic, -

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

Sequence coeh1atuojp5h

-9, -5, -3, -2, -2, -2, -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, 0, 0, more...

integer, monotonic, -

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

Sequence b5l42yip2c5pf

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

integer, monotonic, -

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

Sequence vzgoqbktm1sie

-8, -4, -3, -2, -2, -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, 0, 0, 0, 0, more...

integer, monotonic, -

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

Sequence z0bl3431zlezh

-8, -4, -3, -2, -2, -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, 0, 0, 0, 0, 0, more...

integer, monotonic, -

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

Sequence lcfllsn2225be

-7, -4, -2, -2, -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, 0, 0, 0, 0, 0, 0, more...

integer, monotonic, -

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

Sequence rjzzhkuha5fkb

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

integer, monotonic, -

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

Sequence hfhix3qrfgugc

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

integer, monotonic, -

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

Sequence geipqxsttvn1e

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

integer, monotonic, -

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

Sequence cll2cvcspod2i

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

integer, monotonic, -

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

Sequence zaq3ngr3h5m3c

-5, -2, -2, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

integer, monotonic, -

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

Sequence zuxwsui4of1qm

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

integer, monotonic, -

a(n)=-round(4/n)
n≥1
5 operations
Arithmetic

Sequence 3mpwcyxsu20th

-4, -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, 0, 0, more...

integer, monotonic, -

a(n)=round(-4/n)
n≥1
5 operations
Arithmetic

Sequence 4pqsckeqvmske

-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, 0, more...

integer, monotonic, -

a(n)=-round(3/n)
n≥1
5 operations
Arithmetic

Sequence uiwpbupm4ms4e

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, -16, more...

integer, monotonic, -

a(n)=round(-n/3)
n≥0
5 operations
Arithmetic
a(n)=∑[-C(a(n-1), a(n-2))]
a(0)=0
a(1)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=floor((sqrt(2)-n)/3)
n≥0
7 operations
Power

Sequence nstm41puc5tnf

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, -12, -12, more...

integer, monotonic, -

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

Sequence ua1sgqltpgmpo

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, -12, more...

integer, monotonic, -

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

Sequence a0d0idtqqqmmc

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, -10, -10, more...

integer, monotonic, -

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

Sequence ggps3eqcdy2mh

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, -8, -8, -8, more...

integer, monotonic, -

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

Sequence qhttwkobu3byd

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, -8, -8, more...

integer, monotonic, -

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

Sequence pxpocjh3utk1g

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, -7, -7, -7, more...

integer, monotonic, -

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

Sequence vqiogtody05gf

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, -6, -6, -6, -6, more...

integer, monotonic, -

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

Sequence iheqmcyfae25o

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, -6, -6, -6, more...

integer, monotonic, -

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

Sequence tbxi3d0jj4q0o

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

integer, monotonic, -

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

Sequence lklrddu15eggg

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

integer, monotonic, -

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

Sequence i4apt40fvwyfd

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

integer, monotonic, -

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

Sequence eyzxf4nd4exkf

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

integer, monotonic, +, A211668

a(n)=floor(sinh(atan(n)))
n≥0
4 operations
Trigonometric
a(n)=round(log(log2(p(n))))
p(n)=nth prime
n≥1
5 operations
Prime
a(n)=round(2-5/n)
n≥2
6 operations
Arithmetic
a(n)=round(root(8, C(n, 2)))
C(n,k)=binomial coefficient
root(n,a)=the n-th root of a
n≥0
6 operations
Combinatoric
a(n)=char[7^n]+a(n-1)
a(0)=0
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive

Sequence r3v3bznyla3rk

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

integer, monotonic, +, A211669

a(n)=ceil(log(sqrt(n)))
n≥1
4 operations
Power
a(n)=floor(sinh(atan(n)))
n≥1
4 operations
Trigonometric
a(n)=2-round(4/n)
n≥2
6 operations
Arithmetic
a(n)=∑[C(9, lcm(n, 9))]
lcm(a,b)=least common multiple
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥2
6 operations
Combinatoric
a(n)=round(root(8, C(n, 2)))
C(n,k)=binomial coefficient
root(n,a)=the n-th root of a
n≥1
6 operations
Combinatoric

Sequence 5ahjijk02n0zh

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

integer, monotonic, +

a(n)=∑[xor(a(n-1), a(n-2))]
a(0)=1
a(1)=0
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=and(1, a(n-2))+a(n-1)
a(0)=1
a(1)=1
and(a,b)=bitwise and
n≥0
5 operations
Recursive
a(n)=∑[sqrt(xor(a(n-1), a(n-2)))]
a(0)=1
a(1)=0
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[stern(xor(a(n-1), a(n-2)))]
a(0)=1
a(1)=0
xor(a,b)=bitwise exclusive or
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=round(2/(3/n))
n≥1
6 operations
Arithmetic

Sequence d2nmqdwlp2agj

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

integer, monotonic, +, A211664

a(n)=ceil(sinh(atan(n)))
n≥1
4 operations
Trigonometric
a(n)=floor(exp(root(20, n)))
root(n,a)=the n-th root of a
n≥0
5 operations
Power
a(n)=3-round(4/n)
n≥2
6 operations
Arithmetic
a(n)=xor(3, round(4/n))
xor(a,b)=bitwise exclusive or
n≥2
6 operations
Bitwise
a(n)=stern(or(1, ceil(log2(n))))
or(a,b)=bitwise or
stern(n)=Stern-Brocot sequence
n≥2
6 operations
Recursive

Sequence sfeaihgbyqnrj

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

integer, monotonic, +-

a(n)=round(log2(log(p(n))))
p(n)=nth prime
n≥1
5 operations
Prime
a(n)=2-round(3/n)
n≥1
6 operations
Arithmetic

Sequence f2qxn3qolkrb

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

integer, monotonic, +, A186313 (multiple)

a(n)=ceil(log2(log2(p(n))))
p(n)=nth prime
n≥1
5 operations
Prime
a(n)=3-round(3/n)
n≥1
6 operations
Arithmetic
a(n)=xor(3, round(3/n))
xor(a,b)=bitwise exclusive or
n≥1
6 operations
Bitwise
a(n)=floor(4/root(n, 6))
root(n,a)=the n-th root of a
n≥1
6 operations
Power
a(n)=∑[ceil(Λ(φ(p(n))))]
p(n)=nth prime
ϕ(n)=number of relative primes (Euler's totient)
Λ(n)=Von Mangoldt's function
∑(a)=partial sums of a
n≥1
6 operations
Prime

Sequence m4hrskoynob5o

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

integer, monotonic, +, A230864

a(n)=∑[char[2^a(n-1)]]
a(0)=1
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[char[a(n-1)^a(n-2)]]
a(0)=1
a(1)=2
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[char[a(n-1)^a(n-3)]]
a(0)=1
a(1)=2
a(2)=2
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=round(4-9/n)
n≥2
6 operations
Arithmetic
a(n)=round(4/root(n, 9))
root(n,a)=the n-th root of a
n≥1
6 operations
Power

Sequence 0fuodznectink

0, 1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 58, 59, more...

integer, strictly-monotonic, +, A047263

a(n)=round(n*ζ(3))
ζ(n)=Riemann zeta
n≥0
5 operations
Prime
a(n)=round(6*n/5)
n≥0
6 operations
Arithmetic
a(n)=round(n*root(6, 3))
root(n,a)=the n-th root of a
n≥0
6 operations
Power
a(n)=gcd(n, 5)%3+a(n-1)
a(0)=0
gcd(a,b)=greatest common divisor
n≥2
7 operations
Recursive
a(n)=∑[pt(n%5+a(n-1))]
a(0)=0
pt(n)=Pascals triangle by rows
∑(a)=partial sums of a
n≥0
7 operations
Combinatoric

Sequence jsb3hwm1o4w1n

0, 2, 3, 5, 7, 8, 10, 12, 13, 15, 17, 18, 20, 22, 23, 25, 27, 28, 30, 32, 33, 35, 37, 38, 40, 42, 43, 45, 47, 48, 50, 52, 53, 55, 57, 58, 60, 62, 63, 65, 67, 68, 70, 72, 73, 75, 77, 78, 80, 82, more...

integer, strictly-monotonic, +, A047222

a(n)=∑[stern(a(n-1)+a(n-2))]
a(0)=0
a(1)=2
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[agc(a(n-1)+a(n-2))]
a(0)=0
a(1)=2
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
5 operations
Prime
a(n)=∑[φ(or(a(n-1), a(n-2)))]
a(0)=0
a(1)=2
or(a,b)=bitwise or
ϕ(n)=number of relative primes (Euler's totient)
∑(a)=partial sums of a
n≥0
5 operations
Prime
a(n)=round(5*n/3)
n≥0
6 operations
Arithmetic
a(n)=round(n*root(e, 4))
e=2.7182... (Euler e)
root(n,a)=the n-th root of a
n≥0
6 operations
Power

Sequence adb5hwvfflnci

0, 2, 5, 7, 9, 12, 14, 16, 19, 21, 23, 26, 28, 30, 33, 35, 37, 40, 42, 44, 47, 49, 51, 54, 56, 58, 61, 63, 65, 68, 70, 72, 75, 77, 79, 82, 84, 86, 89, 91, 93, 96, 98, 100, 103, 105, 107, 110, 112, 114, more...

integer, strictly-monotonic, +, A047386

a(n)=∑[p(gcd(a(n-1), a(n-2)))]
a(0)=0
a(1)=2
gcd(a,b)=greatest common divisor
p(n)=nth prime
∑(a)=partial sums of a
n≥0
5 operations
Prime
a(n)=round(7*n/3)
n≥0
6 operations
Arithmetic
a(n)=round(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(∑[2+a(n-1)/7])
a(0)=0
∑(a)=partial sums of a
n≥0
7 operations
Recursive
a(n)=floor(∑[6+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 5itnt1tqrjtcd

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

integer, monotonic, +, A248103

a(n)=and(1, a(n-2))+a(n-1)
a(0)=1
a(1)=2
and(a,b)=bitwise and
n≥0
5 operations
Recursive
a(n)=2+a(n-3)%a(n-1)
a(0)=1
a(1)=2
a(2)=3
n≥0
5 operations
Recursive
a(n)=a(n-3)+lpf(φ(a(n-1)))
a(0)=1
a(1)=2
a(2)=3
ϕ(n)=number of relative primes (Euler's totient)
lpf(n)=least prime factor of n
n≥0
5 operations
Prime
a(n)=round(2/(3/n))
n≥2
6 operations
Arithmetic
a(n)=ceil(n/root(4, 5))
root(n,a)=the n-th root of a
n≥1
6 operations
Power

Sequence sy5qdog4eadxg

2, 3, 5, 7, 8, 10, 12, 13, 15, 17, 18, 20, 22, 23, 25, 27, 28, 30, 32, 33, 35, 37, 38, 40, 42, 43, 45, 47, 48, 50, 52, 53, 55, 57, 58, 60, 62, 63, 65, 67, 68, 70, 72, 73, 75, 77, 78, 80, 82, 83, more...

integer, strictly-monotonic, +, A028738 (multiple)

a(n)=∑[stern(a(n-1)+a(n-2))]
a(0)=2
a(1)=1
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[agc(a(n-1)+a(n-2))]
a(0)=2
a(1)=1
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
5 operations
Prime
a(n)=∑[φ(or(a(n-1), a(n-2)))]
a(0)=2
a(1)=1
or(a,b)=bitwise or
ϕ(n)=number of relative primes (Euler's totient)
∑(a)=partial sums of a
n≥0
5 operations
Prime
a(n)=round(5/(3/n))
n≥1
6 operations
Arithmetic
a(n)=round(n*root(e, 4))
e=2.7182... (Euler e)
root(n,a)=the n-th root of a
n≥1
6 operations
Power

Sequence mohayvddhln

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, 1, more...

integer, monotonic, +

a(n)=round(3/log(n))
n≥2
5 operations
Power
a(n)=round(1+3/n)
n≥1
6 operations
Arithmetic

Sequence nx50iidf51pnn

-3, -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, more...

integer, monotonic, +-

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

Sequence hsjbn5nrnevlk

-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, 14, 14, more...

integer, monotonic, +-

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

Sequence d0xn5ulif0fri

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

integer, monotonic, +-

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

Sequence hhnh2octlmmsg

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

integer, monotonic, -

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

Sequence asycujffciuco

0, 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, more...

decimal, monotonic, +

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

Sequence erzuw11sr55sp

0, 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, more...

decimal, monotonic, +

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

Sequence u5biptv10mhrh

0, 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, more...

integer, monotonic, +

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

Sequence 04acqctcm4fxn

0, 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, more...

integer, monotonic, +

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

Sequence 11m22puolr14p

0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, more...

integer, strictly-monotonic, +, A047588

a(n)=round(8*n/7)
n≥0
6 operations
Arithmetic
a(n)=round(n*∑[a(n-1)/8])
a(0)=1
∑(a)=partial sums of a
n≥0
7 operations
Recursive
a(n)=∑[pt(n%7*a(n-1))]
a(0)=0
pt(n)=Pascals triangle by rows
∑(a)=partial sums of a
n≥0
7 operations
Combinatoric

Sequence dbdzaixs0sa4f

0, 1, 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, more...

integer, strictly-monotonic, +, A047318

a(n)=round(7*n/6)
n≥0
6 operations
Arithmetic
a(n)=round(n*root(7, 3))
root(n,a)=the n-th root of a
n≥0
6 operations
Power
a(n)=floor(sqrt(∑[e+a(n-1)]))
a(0)=0
e=2.7182... (Euler e)
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=∑[pt(n%6+a(n-1))]
a(0)=0
pt(n)=Pascals triangle by rows
∑(a)=partial sums of a
n≥0
7 operations
Combinatoric
a(n)=∑[ω(n%6+a(n-1))]
a(0)=0
ω(n)=number of distinct prime divisors of n
∑(a)=partial sums of a
n≥2
7 operations
Prime

Sequence ay4fgfxyhz4ib

0, 1, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, more...

integer, strictly-monotonic, +, A047207

a(n)=round(5*n/4)
n≥0
6 operations
Arithmetic
a(n)=round(n*root(8, 6))
root(n,a)=the n-th root of a
n≥0
6 operations
Power
a(n)=ceil(n+a(n-1)/5)
a(0)=0
n≥0
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≥1
6 operations
Prime
a(n)=∑[gcd(n, ∑[n]+a(n-1))]
a(0)=0
∑(a)=partial sums of a
gcd(a,b)=greatest common divisor
n≥0
7 operations
Recursive

Sequence 2feoapiywvy1e

0, 1, 3, 4, 6, 7, 8, 10, 11, 13, 14, 15, 17, 18, 20, 21, 22, 24, 25, 27, 28, 29, 31, 32, 34, 35, 36, 38, 39, 41, 42, 43, 45, 46, 48, 49, 50, 52, 53, 55, 56, 57, 59, 60, 62, 63, 64, 66, 67, 69, more...

integer, strictly-monotonic, +, A047299

a(n)=round(7*n/5)
n≥0
6 operations
Arithmetic
a(n)=ceil(∑[sqrt(ϕ^a(n-1))])
a(0)=0
ϕ GoldenRatio=1.618... (Golden Ratio)
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=ceil(∑[sqrt(ϕ)^a(n-1)])
a(0)=0
ϕ GoldenRatio=1.618... (Golden Ratio)
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=round(∑[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)=floor(n+(a(n-1)+a(n-2))/7)
a(0)=0
a(1)=1
n≥1
8 operations
Recursive

Sequence x1ed3xl0fpmkp

0, 1, 3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 17, 19, 20, 21, 23, 24, 26, 27, 29, 30, 31, 33, 34, 36, 37, 39, 40, 41, 43, 44, 46, 47, 49, 50, 51, 53, 54, 56, 57, 59, 60, 61, 63, 64, 66, 67, 69, 70, more...

integer, strictly-monotonic, +, A275672 (weak, multiple)

a(n)=round(10*n/7)
n≥0
6 operations
Arithmetic
a(n)=a(n-2)+Ω(9-gcd(a(n-1), 5))
a(0)=0
a(1)=1
gcd(a,b)=greatest common divisor
Ω(n)=number of prime divisors of n
n≥0
8 operations
Prime
a(n)=a(n-2)+gpf(7-gcd(a(n-1), 5))
a(0)=0
a(1)=1
gcd(a,b)=greatest common divisor
gpf(n)=greatest prime factor of n
n≥0
8 operations
Prime
a(n)=a(n-2)+τ(8+gcd(a(n-1), 5))
a(0)=0
a(1)=1
gcd(a,b)=greatest common divisor
τ(n)=number of divisors of n
n≥0
8 operations
Prime

Sequence i0req5z2sfl1j

0, 2, 3, 5, 6, 8, 10, 11, 13, 14, 16, 18, 19, 21, 22, 24, 26, 27, 29, 30, 32, 34, 35, 37, 38, 40, 42, 43, 45, 46, 48, 50, 51, 53, 54, 56, 58, 59, 61, 62, 64, 66, 67, 69, 70, 72, 74, 75, 77, 78, more...

integer, strictly-monotonic, +, A047448

a(n)=round(8*n/5)
n≥0
6 operations
Arithmetic
a(n)=round(n*log(3)^5)
n≥0
7 operations
Power
a(n)=floor(∑[9-ω(a(n-1))]/5)
a(0)=1
ω(n)=number of distinct prime divisors of n
∑(a)=partial sums of a
n≥0
8 operations
Prime

Sequence g3bzyyy3pwizm

0, 2, 4, 5, 7, 9, 11, 12, 14, 16, 18, 19, 21, 23, 25, 26, 28, 30, 32, 33, 35, 37, 39, 40, 42, 44, 46, 47, 49, 51, 53, 54, 56, 58, 60, 61, 63, 65, 67, 68, 70, 72, 74, 75, 77, 79, 81, 82, 84, 86, more...

integer, strictly-monotonic, +, A047379

a(n)=round(7*n/4)
n≥0
6 operations
Arithmetic
a(n)=ceil(∑[log(4+a(n-1))])
a(0)=0
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=ceil(∑[(7+a(n-1))/5])
a(0)=0
∑(a)=partial sums of a
n≥0
7 operations
Recursive
a(n)=gcd(C(n, 3), 2)+a(n-1)
a(0)=0
C(n,k)=binomial coefficient
gcd(a,b)=greatest common divisor
n≥0
7 operations
Combinatoric
a(n)=∑[xor(3, gcd(∑[n], a(n-1)))]
a(0)=0
∑(a)=partial sums of a
gcd(a,b)=greatest common divisor
xor(a,b)=bitwise exclusive or
n≥1
7 operations
Recursive

Sequence jny5vguodxjxb

0, 3, 5, 8, 11, 13, 16, 19, 21, 24, 27, 29, 32, 35, 37, 40, 43, 45, 48, 51, 53, 56, 59, 61, 64, 67, 69, 72, 75, 77, 80, 83, 85, 88, 91, 93, 96, 99, 101, 104, 107, 109, 112, 115, 117, 120, 123, 125, 128, 131, more...

integer, strictly-monotonic, +, A047622

a(n)=round(8*n/3)
n≥0
6 operations
Arithmetic
a(n)=round(n*2^sqrt(2))
n≥0
7 operations
Power
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≥1
7 operations
Prime
a(n)=∑[4-φ(gcd(n, a(n-1)))]
a(0)=0
gcd(a,b)=greatest common divisor
ϕ(n)=number of relative primes (Euler's totient)
∑(a)=partial sums of a
n≥1
7 operations
Prime
a(n)=floor(Δ[a(n-1)/4+n²])
a(0)=1
Δ(a)=differences of a
n≥0
8 operations
Recursive

Sequence qfgxrrwrks0fm

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

integer, monotonic, +-

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

Sequence 5xfyhzn0zzhfn

1, 0.6666666666666666, 0.3333333333333333, 0.3333333333333333, 0.3333333333333333, 0.3333333333333333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

decimal, monotonic, +

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

Sequence ghdziiqdodvde

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, 10, 11, 11, 11, more...

integer, monotonic, +, A075249

a(n)=round(1+n/5)
n≥1
6 operations
Arithmetic
a(n)=char[5+a(n-1)]+a(n-1)
a(0)=1
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive
a(n)=ceil((n+sqrt(2))/5)
n≥2
7 operations
Power
a(n)=τ(2^round(n/5))
τ(n)=number of divisors of n
n≥1
7 operations
Prime
a(n)=C(n, 4)%5+a(n-1)
a(0)=1
C(n,k)=binomial coefficient
n≥2
7 operations
Combinatoric

Sequence m1bt1j2vuq33h

1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, more...

integer, strictly-monotonic, +, A092784

a(n)=round(8/(7/n))
n≥1
6 operations
Arithmetic
a(n)=round(n*∑[a(n-1)/8])
a(0)=1
∑(a)=partial sums of a
n≥1
7 operations
Recursive
a(n)=∑[ω(2+n%7)]
ω(n)=number of distinct prime divisors of n
∑(a)=partial sums of a
n≥1
7 operations
Prime
a(n)=∑[pt(--n%7)]
pt(n)=Pascals triangle by rows
∑(a)=partial sums of a
n≥1
7 operations
Combinatoric
a(n)=∑[agc(2^(n%7))]
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
7 operations
Prime

Sequence 1a11uqjq0141b

1.5, 1, 0.5, 0.5, 0.5, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, more...

decimal, monotonic, +

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

Sequence 5l0zt3taq3sxi

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

integer, monotonic, +-

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

Sequence hbyy5yfleys0k

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, -14, -14, more...

integer, monotonic, +-

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

Sequence jnsep0mgydogj

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, 18, 18, more...

integer, monotonic, +

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

Sequence qumck5cbl2w1d

3, 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, more...

integer, monotonic, +-

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

[0] [1] [2] [3] [4] ... [234]