Sequence Database

A database with 1693109 machine generated integer and decimal sequences.

Displaying result 0-99 of total 70802. [0] [1] [2] [3] [4] ... [708]

Sequence uuh2g5lkrdn1p

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, +, A054899

a(n)=floor(n/10)
n≥0
4 operations
Arithmetic
a(n)=floor(n/π²)
π=3.1415... (Pi)
n≥0
5 operations
Power

Sequence xkc30mx3g1elh

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, +, A054898

a(n)=floor(n/9)
n≥0
4 operations
Arithmetic
a(n)=floor(n*(1/3)²)
n≥0
7 operations
Power

Sequence myteev5kwyurj

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, +, A054897

a(n)=floor(n/8)
n≥0
4 operations
Arithmetic
a(n)=or(7, n)%7
or(a,b)=bitwise or
n≥0
5 operations
Divisibility

Sequence 2wh5oq4sw0uum

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, +, A132270

a(n)=floor(n/7)
n≥0
4 operations
Arithmetic

Sequence 3lybwm34gm1nd

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, +, A152467

a(n)=floor(n/6)
n≥0
4 operations
Arithmetic

Sequence 1pzrt1brbvpqo

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, +, A002266

a(n)=floor(n/5)
n≥0
4 operations
Arithmetic
a(n)=∑[char[5+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 ucgvqrx0u1tac

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, +, A002265

a(n)=floor(n/4)
n≥0
4 operations
Arithmetic
a(n)=∑[char[4+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)=floor(n*(1/2)²)
n≥0
7 operations
Power

Sequence qvrfgamnumekh

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, +, A002264

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

Sequence 3mssrddd33j3l

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, +, A004526

a(n)=floor(n/2)
n≥0
4 operations
Arithmetic
a(n)=floor(sinh(log(n)))
n≥1
4 operations
Trigonometric
a(n)=∑[a(n-2)^a(n-1)]
a(0)=0
a(1)=0
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=n-1-a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=a(n-2)+C(a(n-1), n)
a(0)=0
a(1)=0
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric

Sequence d3ww0hupuvitm

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, +, A033326

a(n)=floor(6/n)
n≥1
4 operations
Arithmetic
a(n)=floor(exp(3)/(3*n))
n≥1
7 operations
Power

Sequence ifwghe5my5mwp

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, +, A033327

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

Sequence ytbf3sx21l5di

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, +, A033328

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

Sequence 1byu5owrxjkgb

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, +, A033329

a(n)=floor(9/n)
n≥1
4 operations
Arithmetic
a(n)=floor(π²/n)
π=3.1415... (Pi)
n≥1
5 operations
Power

Sequence hmgw3xwv4uile

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, +, A033330

a(n)=floor(10/n)
n≥1
4 operations
Arithmetic
a(n)=floor(exp(3)/(2*n))
n≥1
7 operations
Power

Sequence am0zotyybvy5i

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

integer, monotonic, +, A032615

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

Sequence zdyrvy23ooe2d

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

integer, monotonic, +, A032634

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

Sequence bc51ancmpe3hf

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

integer, monotonic, +, A038128

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

Sequence 5qsh3q5aueqwo

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

integer, monotonic, +, A060143

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

Sequence szqkfbzepdyng

0, 1, 3, 4, 6, 8, 9, 11, 12, 14, 16, 17, 19, 21, 22, 24, 25, 27, 29, 30, 32, 33, 35, 37, 38, 40, 42, 43, 45, 46, 48, 50, 51, 53, 55, 56, 58, 59, 61, 63, 64, 66, 67, 69, 71, 72, 74, 76, 77, 79, more...

integer, strictly-monotonic, +, A066096

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

Sequence s0lxj01srnldo

0, 1, 3, 5, 6, 8, 10, 12, 13, 15, 17, 19, 20, 22, 24, 25, 27, 29, 31, 32, 34, 36, 38, 39, 41, 43, 45, 46, 48, 50, 51, 53, 55, 57, 58, 60, 62, 64, 65, 67, 69, 71, 72, 74, 76, 77, 79, 81, 83, 84, more...

integer, strictly-monotonic, +

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

Sequence qnlyu4e2kydck

0, 2, 5, 8, 10, 13, 16, 19, 21, 24, 27, 29, 32, 35, 38, 40, 43, 46, 48, 51, 54, 57, 59, 62, 65, 67, 70, 73, 76, 78, 81, 84, 86, 89, 92, 95, 97, 100, 103, 106, 108, 111, 114, 116, 119, 122, 125, 127, 130, 133, more...

integer, strictly-monotonic, +, A022843

a(n)=floor(n*e)
e=2.7182... (Euler e)
n≥0
4 operations
Arithmetic

Sequence 0ys2t2405c51g

0, 3, 6, 9, 12, 15, 18, 21, 25, 28, 31, 34, 37, 40, 43, 47, 50, 53, 56, 59, 62, 65, 69, 72, 75, 78, 81, 84, 87, 91, 94, 97, 100, 103, 106, 109, 113, 116, 119, 122, 125, 128, 131, 135, 138, 141, 144, 147, 150, 153, more...

integer, strictly-monotonic, +, A022844

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

Sequence lbd4hcqbi1xik

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, -

a(n)=-(n+a(n-1))
a(0)=0
n≥0
4 operations
Recursive
a(n)=floor(-n/2)
n≥0
5 operations
Arithmetic
a(n)=∑[-and(1, n)]
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
5 operations
Bitwise
a(n)=∑[-n%2]
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑[xor(-1, a(n-1))]
a(0)=0
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence o2jat0xtdbkon

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

Sequence ayyztminn21cp

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

Sequence yvlrhgrxyvajn

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

Sequence byv0b0g0buorg

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

Sequence gakheolrgqdbl

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)=floor(-n/3)
n≥0
5 operations
Arithmetic
a(n)=a(n-1)-char[3*n]
a(0)=0
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive
a(n)=floor((log(2)-n)/3)
n≥0
7 operations
Power

Sequence 3pnayfgz5srro

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, -

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

Sequence oaxq0oqukzeof

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)=floor(-n/5)
n≥0
5 operations
Arithmetic

Sequence svoxauiagtfg

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

Sequence q020pkyri1f5k

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

Sequence aoh5oroajzhji

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, -

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

Sequence 3urygk353s1zd

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

Sequence vzjjndhymkhhb

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)=floor(-n/10)
n≥0
5 operations
Arithmetic
a(n)=floor(n*(1-log(3)))
n≥0
7 operations
Power

Sequence texjg1xckplrb

0, 0, 2, 2, 4, 4, 6, 6, 8, 8, 10, 10, 12, 12, 14, 14, 16, 16, 18, 18, 20, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 32, 32, 34, 34, 36, 36, 38, 38, 40, 40, 42, 42, 44, 44, 46, 46, 48, 48, more...

integer, monotonic, +, A052928

a(n)=and(62, n)
and(a,b)=bitwise and
n≥0
3 operations
Bitwise
a(n)=n-n%2
n≥0
5 operations
Divisibility
a(n)=gcd(a(n-1), 2)+a(n-2)
a(0)=0
a(1)=0
gcd(a,b)=greatest common divisor
n≥0
5 operations
Recursive
a(n)=2*floor(n/2)
n≥0
6 operations
Arithmetic
a(n)=n-and(1, n)²
and(a,b)=bitwise and
n≥0
6 operations
Power

Sequence a25wy4uqfpkvc

0, 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, more...

integer, monotonic, +

a(n)=n-n%3
n≥0
5 operations
Divisibility
a(n)=3*floor(n/3)
n≥0
6 operations
Arithmetic

Sequence zvjz3ymnc34ci

0, 0, 3, 3, 6, 6, 9, 9, 12, 12, 15, 15, 18, 18, 21, 21, 24, 24, 27, 27, 30, 30, 33, 33, 36, 36, 39, 39, 42, 42, 45, 45, 48, 48, 51, 51, 54, 54, 57, 57, 60, 60, 63, 63, 66, 66, 69, 69, 72, 72, more...

integer, monotonic, +

a(n)=gcd(a(n-1), 3)+a(n-2)
a(0)=0
a(1)=0
gcd(a,b)=greatest common divisor
n≥0
5 operations
Recursive
a(n)=3*floor(n/2)
n≥0
6 operations
Arithmetic

Sequence adnmbythco1qg

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, -16, more...

integer, monotonic, +-

a(n)=a(n-3)-C(9, a(n-1))
a(0)=1
a(1)=0
a(2)=0
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=floor(a(n-3)-exp(a(n-1)))
a(0)=1
a(1)=0
a(2)=0
n≥0
5 operations
Recursive
a(n)=floor(1-n/3)
n≥0
6 operations
Arithmetic
a(n)=a(n-1)-char[3*n]
a(0)=1
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive
a(n)=floor(log(3)-n/3)
n≥0
7 operations
Power

Sequence vgg1wbsxslptc

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, -22, -23, -23, more...

integer, monotonic, +-

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

Sequence an2k3pxzungqb

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, -15, more...

integer, monotonic, +-

a(n)=a(n-3)-C(a(n-1), 2)
a(0)=1
a(1)=1
a(2)=1
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=1-floor(n/3)
n≥0
6 operations
Arithmetic
a(n)=floor(sqrt(3)-n/3)
n≥0
7 operations
Power

Sequence aquh5dumxfil

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, -22, -23, more...

integer, monotonic, +-

a(n)=4-n-a(n-1)
a(0)=2
n≥0
5 operations
Recursive
a(n)=∑[μ(5+a(n-1))]
a(0)=2
μ(n)=Möbius function
∑(a)=partial sums of a
n≥0
5 operations
Prime
a(n)=a(n-2)-C(a(n-1), 2)
a(0)=2
a(1)=1
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=floor(2-n/2)
n≥0
6 operations
Arithmetic
a(n)=2-∑[and(1, n)]
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
6 operations
Bitwise

Sequence nbi3y0rjkl01k

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, -22, more...

integer, monotonic, +-

a(n)=5-n-a(n-1)
a(0)=2
n≥0
5 operations
Recursive
a(n)=a(n-2)-C(a(n-1), 2)
a(0)=2
a(1)=2
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=2-floor(n/2)
n≥0
6 operations
Arithmetic

Sequence bugzxfmr4woxm

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)=6-n-a(n-1)
a(0)=3
n≥0
5 operations
Recursive
a(n)=floor(3-n/2)
n≥0
6 operations
Arithmetic
a(n)=3-∑[and(1, n)]
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
6 operations
Bitwise

Sequence mjue1qid2lvog

3, 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, more...

integer, monotonic, +-

a(n)=7-n-a(n-1)
a(0)=3
n≥0
5 operations
Recursive
a(n)=∑[μ(5+a(n-1))]
a(0)=3
μ(n)=Möbius function
∑(a)=partial sums of a
n≥0
5 operations
Prime
a(n)=3-floor(n/2)
n≥0
6 operations
Arithmetic

Sequence o0dgtykehbygc

-3, -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, more...

integer, monotonic, +-

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

Sequence y2vo4s2fqaiz

-3, -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, more...

integer, monotonic, +-

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

Sequence fjy1nvqdabysg

-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, 14, more...

integer, monotonic, +-

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

Sequence pdt3rprn0zfjn

-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, 22, more...

integer, monotonic, +-

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

Sequence otcmwcumywiec

-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, 22, 23, more...

integer, monotonic, +-

a(n)=floor((n-3)/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)=∑[1-a(n-1)]-2
a(0)=0
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=floor(n/2-sqrt(2))
n≥0
7 operations
Power
a(n)=floor(n/2)%n-2
n≥1
8 operations
Divisibility

Sequence bs5yuo3vy5uqb

-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, 15, more...

integer, monotonic, +-

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

Sequence 5dbz00y45jk2o

-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)=floor((n-2)/3)
n≥0
6 operations
Arithmetic
a(n)=n-∑[xor(a(n-1), a(n-2))]
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((n-sqrt(2))/3)
n≥0
7 operations
Power

Sequence uiptobaumv12h

-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, 22, 23, 23, more...

integer, monotonic, +-

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

Sequence cs0aykpea0fpn

-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, 16, more...

integer, monotonic, +-

a(n)=floor((n-1)/3)
n≥0
6 operations
Arithmetic
a(n)=floor((n-log(2))/3)
n≥0
7 operations
Power

Sequence frfyrct43ix2c

-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, 22, 23, 23, 24, more...

integer, monotonic, +-

a(n)=floor((n-1)/2)
n≥0
6 operations
Arithmetic
a(n)=∑[and(1, n)]-1
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
6 operations
Bitwise
a(n)=∑[1-a(n-1)]-1
a(0)=0
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=(n-gcd(n, 2))/2
gcd(a,b)=greatest common divisor
n≥0
7 operations
Divisibility
a(n)=floor((n-log(2))/2)
n≥0
7 operations
Power

Sequence uvt5ouer111wg

0, 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, more...

decimal, monotonic, +

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

Sequence bdcxvfirumx3f

0, 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, more...

decimal, monotonic, +

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

Sequence hedhs12v4d0fl

0, 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, more...

integer, monotonic, +

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

Sequence 3dszjks43by1n

0, 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, more...

decimal, monotonic, +

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

Sequence vyiltw2u2tuyi

0, 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, more...

decimal, monotonic, +

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

Sequence jmztmbvayxtbi

1, 1, 0.5, 0.5, 0.3333333333333333, 0.3333333333333333, 0.25, 0.25, 0.2, 0.2, 0.16666666666666666, 0.16666666666666666, 0.14285714285714285, 0.14285714285714285, 0.125, 0.125, 0.1111111111111111, 0.1111111111111111, 0.1, 0.1, 0.09090909090909091, 0.09090909090909091, 0.08333333333333333, 0.08333333333333333, 0.07692307692307693, more...

decimal, monotonic, +

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

Sequence nsa2yctca2mnd

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)=floor(2-n/3)
n≥0
6 operations
Arithmetic
a(n)=a(n-1)-char[3*n]
a(0)=2
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive

Sequence vtj20uoffylzd

2, 2, 1, 1, 0.6666666666666666, 0.6666666666666666, 0.5, 0.5, 0.4, 0.4, 0.3333333333333333, 0.3333333333333333, 0.2857142857142857, 0.2857142857142857, 0.25, 0.25, 0.2222222222222222, 0.2222222222222222, 0.2, 0.2, 0.18181818181818182, 0.18181818181818182, 0.16666666666666666, 0.16666666666666666, 0.15384615384615385, more...

decimal, monotonic, +

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

Sequence dfafvc3cmyzcj

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, -14, more...

integer, monotonic, +-

a(n)=2-floor(n/3)
n≥0
6 operations
Arithmetic
a(n)=a(n-1)-char[3+a(n-1)]
a(0)=2
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive

Sequence 2gxaxaapf112p

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, 18, more...

integer, monotonic, +

a(n)=floor(2+n/3)
n≥0
6 operations
Arithmetic
a(n)=char[3+a(n-1)]+a(n-1)
a(0)=2
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive

Sequence dh3iy34twsywf

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

Sequence 3crhzi44kwtob

3, 3, 1.5, 1.5, 1, 1, 0.75, 0.75, 0.6, 0.6, 0.5, 0.5, 0.42857142857142855, 0.42857142857142855, 0.375, 0.375, 0.3333333333333333, 0.3333333333333333, 0.3, 0.3, 0.2727272727272727, 0.2727272727272727, 0.25, 0.25, 0.23076923076923078, more...

decimal, monotonic, +

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

Sequence 4gmc4z1nmvxxk

3, 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, more...

integer, monotonic, +-

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

Sequence ygafpuz2mylue

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, 19, more...

integer, monotonic, +

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

Sequence zizkyu0libjaj

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

integer, monotonic, +, A000195

a(n)=floor(log(n))
n≥1
3 operations
Power

Sequence qlf3d40uqfgeb

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

integer, monotonic, +, A000196

a(n)=floor(sqrt(n))
n≥0
3 operations
Power
a(n)=∑[char[pt(n)²]]
pt(n)=Pascals triangle by rows
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑[char[∑[2+a(n-1)]]]
a(0)=1
∑(a)=partial sums of a
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive
a(n)=τ(n)%2+a(n-1)
a(0)=0
τ(n)=number of divisors of n
n≥0
6 operations
Prime

Sequence kzpxgr055fwee

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

integer, monotonic, +, A000523

a(n)=floor(log2(n))
n≥1
3 operations
Power
a(n)=∑[char[or(n, a(n-1))]]
a(0)=1
or(a,b)=bitwise or
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[char[∑[2*a(n-1)]]]
a(0)=1
∑(a)=partial sums of a
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive

Sequence mwh1dukeiz1ff

1, 2, 7, 20, 54, 148, 403, 1096, 2980, 8103, 22026, 59874, 162754, 442413, 1202604, 3269017, 8886110, 24154952, 65659969, 178482300, 485165195, 1318815734, 3584912846, 9744803446, 26489122129, 72004899337, 195729609428, 532048240601, 1446257064291, 3931334297144, 10686474581524, 29048849665247, 78962960182680, 214643579785916, 583461742527454, 1586013452313430, 4311231547115195, more...

integer, strictly-monotonic, +, A000149

a(n)=floor(exp(n))
n≥0
3 operations
Power
a(n)=floor(exp(n)-a(n-1))+a(n-1)
a(0)=1
n≥0
7 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)=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=3.1415... (Pi)
root(n,a)=the n-th root of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Recursive

Sequence tvabhdxikc3fl

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

integer, monotonic, +, A255270

a(n)=floor(root(4, n))
root(n,a)=the n-th root of a
n≥0
4 operations
Power
a(n)=stern(ceil(sqrt(log2(n))))
stern(n)=Stern-Brocot sequence
n≥1
5 operations
Recursive
a(n)=floor(sqrt(log(p(n))))
p(n)=nth prime
n≥1
5 operations
Prime

Sequence 1hdzh2hh4zvrm

0, 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, 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, +, A048766

a(n)=floor(root(3, n))
root(n,a)=the n-th root of a
n≥0
4 operations
Power

Sequence llkyrrajh4rze

0, -1, -4, -9, -16, -25, -36, -49, -64, -81, -100, -121, -144, -169, -196, -225, -256, -289, -324, -361, -400, -441, -484, -529, -576, -625, -676, -729, -784, -841, -900, -961, -1024, -1089, -1156, -1225, -1296, -1369, -1444, -1521, -1600, -1681, -1764, -1849, -1936, -2025, -2116, -2209, -2304, -2401, more...

integer, strictly-monotonic, -

a(n)=-n²
n≥0
3 operations
Power
a(n)=n*floor(-n)
n≥0
5 operations
Arithmetic
a(n)=a(n-1)-Δ[n²]
a(0)=0
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=∑[or(1, a(n-1)-2)]
a(0)=0
or(a,b)=bitwise or
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=n-lcm(1+n, n)
lcm(a,b)=least common multiple
n≥0
7 operations
Divisibility

Sequence zngyxnx2llm4l

0, 0, 1, 3, 5, 8, 12, 16, 21, 27, 33, 40, 48, 56, 65, 75, 85, 96, 108, 120, 133, 147, 161, 176, 192, 208, 225, 243, 261, 280, 300, 320, 341, 363, 385, 408, 432, 456, 481, 507, 533, 560, 588, 616, 645, 675, 705, 736, 768, 800, more...

integer, monotonic, +, A000212

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)=floor(n²/3)
n≥0
5 operations
Power
a(n)=floor(n*n/3)
n≥0
6 operations
Arithmetic
a(n)=∑[xor(a(n-1), a(n-2))]+a(n-1)
a(0)=0
a(1)=1
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence y4xh0yzjyqhfp

0, 0, 2, 4, 8, 12, 18, 24, 32, 40, 50, 60, 72, 84, 98, 112, 128, 144, 162, 180, 200, 220, 242, 264, 288, 312, 338, 364, 392, 420, 450, 480, 512, 544, 578, 612, 648, 684, 722, 760, 800, 840, 882, 924, 968, 1012, 1058, 1104, 1152, 1200, more...

integer, monotonic, +, A007590

a(n)=∑[a(n-2)]+a(n-1)
a(0)=0
a(1)=2
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=∑[and(n, -2)]
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
5 operations
Bitwise
a(n)=floor(n²/2)
n≥0
5 operations
Power
a(n)=floor(n*n/2)
n≥0
6 operations
Arithmetic
a(n)=∑[2*n]-a(n-1)
a(0)=0
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence hsczirn2nc2gc

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, -

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

Sequence krziieavf2ubc

0, 1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 30, 32, 33, 34, 36, 37, 38, 40, 41, 42, 44, 45, 46, 48, 49, 50, 52, 53, 54, 56, 57, 58, 60, 61, 62, 64, 65, more...

integer, strictly-monotonic, +, A004773

a(n)=4+a(n-3)%a(n-1)
a(0)=0
a(1)=1
a(2)=2
n≥0
5 operations
Recursive
a(n)=floor(n+n/3)
n≥0
6 operations
Arithmetic
a(n)=∑[1+and(a(n-1), a(n-2))]
a(0)=0
a(1)=1
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=∑[gcd(a(n-1)+a(n-2), 2)]
a(0)=0
a(1)=1
gcd(a,b)=greatest common divisor
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=∑[C(2/a(n-1), a(n-2))]
a(0)=0
a(1)=1
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
6 operations
Combinatoric

Sequence glqrw0bmdqurp

0, 1, 3, 5, 8, 12, 16, 21, 27, 33, 40, 48, 56, 65, 75, 85, 96, 108, 120, 133, 147, 161, 176, 192, 208, 225, 243, 261, 280, 300, 320, 341, 363, 385, 408, 432, 456, 481, 507, 533, 560, 588, 616, 645, 675, 705, 736, 768, 800, 833, more...

integer, strictly-monotonic, +

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
5 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
5 operations
Recursive
a(n)=floor(n/(3/n))
n≥1
6 operations
Arithmetic
a(n)=n²-a(n-1)-a(n-2)
a(0)=0
a(1)=1
n≥0
6 operations
Recursive
a(n)=floor((1+n)²/3)
n≥0
7 operations
Power

Sequence mitz1ae2w3fje

0, 2, 4, 8, 12, 18, 24, 32, 40, 50, 60, 72, 84, 98, 112, 128, 144, 162, 180, 200, 220, 242, 264, 288, 312, 338, 364, 392, 420, 450, 480, 512, 544, 578, 612, 648, 684, 722, 760, 800, 840, 882, 924, 968, 1012, 1058, 1104, 1152, 1200, 1250, more...

integer, strictly-monotonic, +

a(n)=∑[∑[2-a(n-1)]]
a(0)=0
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[∑[xor(2, a(n-1))]]
a(0)=0
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[a(n-2)+lpf(a(n-1))]
a(0)=0
a(1)=2
lpf(n)=least prime factor of n
∑(a)=partial sums of a
n≥0
5 operations
Prime
a(n)=floor(n/(2/n))
n≥1
6 operations
Arithmetic
a(n)=∑[n+and(1, n)]
and(a,b)=bitwise and
∑(a)=partial sums of a
n≥0
6 operations
Bitwise

Sequence ppmbkh5y5233f

-2, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, more...

integer, strictly-monotonic, +-

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

Sequence vlheavrivhgjf

-1, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, more...

integer, strictly-monotonic, +-

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

Sequence ogkg5zts1ubuc

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

integer, periodic-12, non-monotonic, +

a(n)=and(2, floor(n/3))
and(a,b)=bitwise and
n≥0
6 operations
Bitwise

Sequence f22shtkd5phxb

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

integer, periodic-12, non-monotonic, +

a(n)=and(3, floor(n/3))
and(a,b)=bitwise and
n≥0
6 operations
Bitwise

Sequence gddlfkqehxdsd

0, 0, 0, 3, 4, 5, 12, 14, 16, 27, 30, 33, 48, 52, 56, 75, 80, 85, 108, 114, 120, 147, 154, 161, 192, 200, 208, 243, 252, 261, 300, 310, 320, 363, 374, 385, 432, 444, 456, 507, 520, 533, 588, 602, 616, 675, 690, 705, 768, 784, more...

integer, monotonic, +, A242669

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

Sequence uuhe0od2rdy4d

0, 0, 0.3333333333333333, 0.25, 0.2, 0.3333333333333333, 0.2857142857142857, 0.25, 0.3333333333333333, 0.3, 0.2727272727272727, 0.3333333333333333, 0.3076923076923077, 0.2857142857142857, 0.3333333333333333, 0.3125, 0.29411764705882354, 0.3333333333333333, 0.3157894736842105, 0.3, 0.3333333333333333, 0.3181818181818182, 0.30434782608695654, 0.3333333333333333, 0.32, more...

decimal, non-monotonic, +

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

Sequence oa1ullvlnmpel

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

integer, non-monotonic, +

a(n)=floor(xor(1, n)/3)
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Bitwise

Sequence jhqlwtt4letfm

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

integer, monotonic, +

a(n)=floor(or(1, n)/3)
or(a,b)=bitwise or
n≥0
6 operations
Bitwise

Sequence rjo3k2sltxvpd

0, 0, 2, 3, 8, 10, 18, 21, 32, 36, 50, 55, 72, 78, 98, 105, 128, 136, 162, 171, 200, 210, 242, 253, 288, 300, 338, 351, 392, 406, 450, 465, 512, 528, 578, 595, 648, 666, 722, 741, 800, 820, 882, 903, 968, 990, 1058, 1081, 1152, 1176, more...

integer, monotonic, +

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

Sequence j3skui11q4czm

0, 0.5, 0.3333333333333333, 0.5, 0.4, 0.5, 0.42857142857142855, 0.5, 0.4444444444444444, 0.5, 0.45454545454545453, 0.5, 0.46153846153846156, 0.5, 0.4666666666666667, 0.5, 0.47058823529411764, 0.5, 0.47368421052631576, 0.5, 0.47619047619047616, 0.5, 0.4782608695652174, 0.5, 0.48, more...

decimal, non-monotonic, convergent, +

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

Sequence 5nh3i5hwr0alf

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

integer, non-monotonic, +

a(n)=floor(xor(2, n)/3)
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Bitwise

Sequence l2doyugge5ffi

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

integer, non-monotonic, +

a(n)=floor(or(2, n)/3)
or(a,b)=bitwise or
n≥0
6 operations
Bitwise

Sequence zrkn0p3bi30dk

1, -1, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32, -33, -34, -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, -50, more...

integer, strictly-monotonic, +-

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

Sequence warhwxb1vkbqi

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

integer, non-monotonic, +

a(n)=floor(xor(3, n)/3)
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Bitwise

Sequence rksgf4grbc5zj

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

integer, non-monotonic, +

a(n)=xor(1, floor(n/2))
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Bitwise

Sequence q4fqa54rvdgcb

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

integer, non-monotonic, +

a(n)=xor(1, floor(n/3))
xor(a,b)=bitwise exclusive or
n≥0
6 operations
Bitwise

Sequence oi1yfypzpwhfm

1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 17, 17, more...

integer, monotonic, +

a(n)=or(1, floor(n/3))
or(a,b)=bitwise or
n≥0
6 operations
Bitwise

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