Sequence Database

A database with 1693109 machine generated integer and decimal sequences.

Displaying result 0-99 of total 21845. [0] [1] [2] [3] [4] ... [218]

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 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)=∑[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

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=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)=∑[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)=∑[and(1, ∑[∑[n]])]
∑(a)=partial sums of a
and(a,b)=bitwise and
n≥0
6 operations
Bitwise
a(n)=ceil(n*(1/2)²)
n≥0
7 operations
Power

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=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)=a(n-3)+C(a(n-1), n)
a(0)=0
a(1)=1
a(2)=1
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric

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=3.1415... (Pi)
n≥1
5 operations
Power

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=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=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=1.618... (Golden Ratio)
n≥0
4 operations
Arithmetic

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=1.618... (Golden Ratio)
n≥0
4 operations
Arithmetic

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=0.5772... (Euler Gamma)
n≥0
4 operations
Arithmetic
a(n)=ceil(n*sqrt(3))
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

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=3.1415... (Pi)
n≥0
4 operations
Arithmetic

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)-C(9, a(n-1))
a(0)=0
a(1)=0
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
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)=∑[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 gl5sf4v3cacfp

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, 75, more...

integer, monotonic, +, A168237

a(n)=∑[3-a(n-1)]
a(0)=0
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=∑[xor(3, a(n-1))]
a(0)=0
xor(a,b)=bitwise exclusive or
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=∑[log2(gcd(a(n-1), 8))]
a(0)=0
gcd(a,b)=greatest common divisor
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑[Ω(gcd(a(n-1), 8))]
a(0)=0
gcd(a,b)=greatest common divisor
Ω(n)=max distinct factors of n
∑(a)=partial sums of a
n≥0
5 operations
Prime
a(n)=3*ceil(n/2)
n≥0
6 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 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)=a(n-3)+C(a(n-1), n)
a(0)=1
a(1)=2
a(2)=2
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=a(n-3)+λ(a(n-1)²)
a(0)=1
a(1)=2
a(2)=2
λ(n)=Liouville's function
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 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

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 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

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

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 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((2+n)/3)
n≥0
6 operations
Arithmetic
a(n)=char[3+a(n-1)]+a(n-1)
a(0)=1
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive
a(n)=char[3+a(n-2)]+a(n-1)
a(0)=1
a(1)=1
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive
a(n)=floor(∑[sqrt(a(n-1)/3)])
a(0)=1
∑(a)=partial sums of a
n≥0
6 operations
Recursive
a(n)=floor(∑[φ(a(n-1))]/3)
a(0)=3
ϕ(n)=number of relative primes (Euler's totient)
∑(a)=partial sums of a
n≥0
6 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 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)=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 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 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 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

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)=char[∑[a(n-2)]²]+a(n-1)
a(0)=0
a(1)=1
∑(a)=partial sums of a
char(a)=characteristic function of a (in range)
n≥0
6 operations
Recursive

Sequence 5nkup5uykhmpj

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

integer, monotonic, +, A029837

a(n)=ceil(log2(n))
n≥1
3 operations
Power
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)²/a(n-2)]]
a(0)=1
a(1)=2
char(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
6 operations
Recursive

Sequence ovqncte3hs5ok

1, 3, 8, 21, 55, 149, 404, 1097, 2981, 8104, 22027, 59875, 162755, 442414, 1202605, 3269018, 8886111, 24154953, 65659970, 178482301, 485165196, 1318815735, 3584912847, 9744803447, 26489122130, 72004899338, 195729609429, 532048240602, 1446257064292, 3931334297145, 10686474581525, 29048849665248, 78962960182681, 214643579785917, 583461742527455, 1586013452313431, 4311231547115195, more...

integer, strictly-monotonic, +, A001671

a(n)=ceil(exp(n))
n≥0
3 operations
Power
a(n)=a(n-1)-floor(a(n-1)-exp(n))
a(0)=1
n≥0
7 operations
Recursive

Sequence ubkde1svxp2tp

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

integer, monotonic, +

a(n)=ceil(root(5, n))
root(n,a)=the n-th root of a
n≥0
4 operations
Power

Sequence d1iutjise1enp

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

integer, monotonic, +

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

Sequence xzepsahl3dcik

0, 1, 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, 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, +

a(n)=ceil(root(3, n))
root(n,a)=the n-th root of a
n≥0
4 operations
Power
a(n)=char[n*n²]+a(n-1)
a(0)=0
char(a)=characteristic function of a (in range)
n≥0
7 operations
Recursive

Sequence ahvr5hesbgdhl

1, 2, 5, 8, 13, 18, 25, 32, 41, 50, 61, 72, 85, 98, 113, 128, 145, 162, 181, 200, 221, 242, 265, 288, 313, 338, 365, 392, 421, 450, 481, 512, 545, 578, 613, 648, 685, 722, 761, 800, 841, 882, 925, 968, 1013, 1058, 1105, 1152, 1201, 1250, more...

integer, strictly-monotonic, +

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

Sequence yubinofxwwxvj

0, 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, more...

integer, monotonic, -

a(n)=a(n-1)-abs(Δ[a(n-3)])
a(0)=0
a(1)=0
a(2)=1
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=ceil(n/3-n)
n≥0
6 operations
Arithmetic

Sequence lxzzxyvfvb5nh

0, 1, 2, 3, 6, 9, 12, 17, 22, 27, 34, 41, 48, 57, 66, 75, 86, 97, 108, 121, 134, 147, 162, 177, 192, 209, 226, 243, 262, 281, 300, 321, 342, 363, 386, 409, 432, 457, 482, 507, 534, 561, 588, 617, 646, 675, 706, 737, 768, 801, more...

integer, strictly-monotonic, +, A008810

a(n)=ceil(n²/3)
n≥0
5 operations
Power
a(n)=ceil(n*n/3)
n≥0
6 operations
Arithmetic

Sequence rqbzerefftuvi

0, 1, 2, 5, 8, 13, 18, 25, 32, 41, 50, 61, 72, 85, 98, 113, 128, 145, 162, 181, 200, 221, 242, 265, 288, 313, 338, 365, 392, 421, 450, 481, 512, 545, 578, 613, 648, 685, 722, 761, 800, 841, 882, 925, 968, 1013, 1058, 1105, 1152, 1201, more...

integer, strictly-monotonic, +, A000982

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

Sequence rbn0tqbc1o1u

2, 0.5, 0.3333333333333333, 0.25, 0.2, 0.16666666666666666, 0.14285714285714285, 0.125, 0.1111111111111111, 0.1, 0.09090909090909091, 0.08333333333333333, 0.07692307692307693, 0.07142857142857142, 0.06666666666666667, 0.0625, 0.058823529411764705, 0.05555555555555555, 0.05263157894736842, 0.05, 0.047619047619047616, 0.045454545454545456, 0.043478260869565216, 0.041666666666666664, 0.04, more...

decimal, strictly-monotonic, convergent, +

a(n)=contfrac[ϕ²]/n
ϕ=1.618... (Golden Ratio)
contfrac(a)=continued fraction of a
n≥1
5 operations
Power
a(n)=ceil(2/n)/n
n≥1
6 operations
Arithmetic
a(n)=C(3-n, n)/n
C(n,k)=binomial coefficient
n≥1
7 operations
Combinatoric
a(n)=1/n+μ(n²)
μ(n)=Möbius function
n≥1
7 operations
Prime

Sequence 10ujppa4jaedo

0, 1, 2, 3, 8, 10, 12, 21, 24, 27, 40, 44, 48, 65, 70, 75, 96, 102, 108, 133, 140, 147, 176, 184, 192, 225, 234, 243, 280, 290, 300, 341, 352, 363, 408, 420, 432, 481, 494, 507, 560, 574, 588, 645, 660, 675, 736, 752, 768, 833, more...

integer, strictly-monotonic, +

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

Sequence k3akwsvjofnkg

0, 1, 2, 6, 8, 15, 18, 28, 32, 45, 50, 66, 72, 91, 98, 120, 128, 153, 162, 190, 200, 231, 242, 276, 288, 325, 338, 378, 392, 435, 450, 496, 512, 561, 578, 630, 648, 703, 722, 780, 800, 861, 882, 946, 968, 1035, 1058, 1128, 1152, 1225, more...

integer, strictly-monotonic, +

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

Sequence apuelg0mstdv

0.3333333333333333, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, more...

decimal, strictly-monotonic, +

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

Sequence lg2avumpzokdk

0.5, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, more...

decimal, strictly-monotonic, +

a(n)=n/ceil(2/n)
n≥1
6 operations
Arithmetic
a(n)=n/ceil(2/n²)
n≥1
7 operations
Power
a(n)=n/(1+μ(n²))
μ(n)=Möbius function
n≥1
7 operations
Prime

Sequence ohwl5yv4yswmp

1, 0.5, 0.3333333333333333, 0.5, 0.4, 0.3333333333333333, 0.42857142857142855, 0.375, 0.3333333333333333, 0.4, 0.36363636363636365, 0.3333333333333333, 0.38461538461538464, 0.35714285714285715, 0.3333333333333333, 0.375, 0.35294117647058826, 0.3333333333333333, 0.3684210526315789, 0.35, 0.3333333333333333, 0.36363636363636365, 0.34782608695652173, 0.3333333333333333, 0.36, more...

decimal, non-monotonic, +

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

Sequence ox2qgt3ua4cuk

1, 0.5, 0.6666666666666666, 0.5, 0.6, 0.5, 0.5714285714285714, 0.5, 0.5555555555555556, 0.5, 0.5454545454545454, 0.5, 0.5384615384615384, 0.5, 0.5333333333333333, 0.5, 0.5294117647058824, 0.5, 0.5263157894736842, 0.5, 0.5238095238095238, 0.5, 0.5217391304347826, 0.5, 0.52, more...

decimal, non-monotonic, +

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

Sequence np1ou4doog2q

1, 2, 1.5, 2, 1.6666666666666667, 2, 1.75, 2, 1.8, 2, 1.8333333333333333, 2, 1.8571428571428572, 2, 1.875, 2, 1.8888888888888888, 2, 1.9, 2, 1.9090909090909092, 2, 1.9166666666666667, 2, 1.9230769230769231, more...

decimal, non-monotonic, convergent, +

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

Sequence ai2tpodccspwb

1, 2, 3, 2, 2.5, 3, 2.3333333333333335, 2.6666666666666665, 3, 2.5, 2.75, 3, 2.6, 2.8, 3, 2.6666666666666665, 2.8333333333333335, 3, 2.7142857142857144, 2.857142857142857, 3, 2.75, 2.875, 3, 2.7777777777777777, more...

decimal, non-monotonic, +

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

Sequence uxluei0cfquon

1, 2, 3, 6, 9, 12, 17, 22, 27, 34, 41, 48, 57, 66, 75, 86, 97, 108, 121, 134, 147, 162, 177, 192, 209, 226, 243, 262, 281, 300, 321, 342, 363, 386, 409, 432, 457, 482, 507, 534, 561, 588, 617, 646, 675, 706, 737, 768, 801, 834, more...

integer, strictly-monotonic, +

a(n)=ceil(n/(3/n))
n≥1
6 operations
Arithmetic
a(n)=ceil(1/(3/n²))
n≥1
7 operations
Power

Sequence 1dlrwpozpiwtg

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

integer, strictly-monotonic, +-

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

Sequence 45hikw1mcqyf

3, 1, 0.3333333333333333, 0.25, 0.2, 0.16666666666666666, 0.14285714285714285, 0.125, 0.1111111111111111, 0.1, 0.09090909090909091, 0.08333333333333333, 0.07692307692307693, 0.07142857142857142, 0.06666666666666667, 0.0625, 0.058823529411764705, 0.05555555555555555, 0.05263157894736842, 0.05, 0.047619047619047616, 0.045454545454545456, 0.043478260869565216, 0.041666666666666664, 0.04, more...

decimal, strictly-monotonic, convergent, +

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

Sequence ydepakr3yxgsg

3, 4, 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, non-monotonic, +

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

Sequence 0sqdzzfxcwedo

0, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 49, 56, 64, 72, 81, 90, 100, 110, 121, 132, 144, 156, 169, 182, 196, 210, 225, 240, 256, 272, 289, 306, 324, 342, 361, 380, 400, 420, 441, 462, 484, 506, 529, 552, 576, 600, 625, more...

integer, strictly-monotonic, +

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

Sequence xczdzfn4zpj0k

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, -

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

Sequence dpjbe344prrpe

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, -

a(n)=ceil(-n*e)
e=2.7182... (Euler e)
n≥0
5 operations
Arithmetic

Sequence om2oisjosqcig

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)=ceil(-n/γ)
γ=0.5772... (Euler Gamma)
n≥0
5 operations
Arithmetic

Sequence rftrzoddmwtfm

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, -

a(n)=ceil(-n*ϕ)
ϕ=1.618... (Golden Ratio)
n≥0
5 operations
Arithmetic

Sequence zkv0wshl2df4h

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, -

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

Sequence 4fsue51v44igp

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, -

a(n)=ceil(-n*γ)
γ=0.5772... (Euler Gamma)
n≥0
5 operations
Arithmetic

Sequence 0ch5eijjhld1

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, -

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

Sequence xyelrdbwdcizk

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, -

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

Sequence wnazhboz3xhxp

0, 1, 1, 1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 16, 18, 19, 21, 24, 26, 28, 30, 33, 36, 38, 41, 44, 47, 50, 53, 57, 60, 63, 67, 71, 75, 78, 82, 87, 91, 95, 99, 104, 109, 113, 118, 123, more...

integer, monotonic, +

a(n)=ceil(∑[n/10])
∑(a)=partial sums of a
n≥0
5 operations
Arithmetic

Sequence vzv0tri2md2bi

0, 1, 1, 1, 2, 2, 3, 4, 4, 5, 7, 8, 9, 11, 12, 14, 16, 17, 19, 22, 24, 26, 29, 31, 34, 37, 39, 42, 46, 49, 52, 56, 59, 63, 67, 70, 74, 79, 83, 87, 92, 96, 101, 106, 110, 115, 121, 126, 131, 137, more...

integer, monotonic, +

a(n)=ceil(∑[n/9])
∑(a)=partial sums of a
n≥0
5 operations
Arithmetic

Sequence w1fkwvy3bwa4m

0, 1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 17, 20, 22, 24, 27, 29, 32, 35, 38, 41, 44, 48, 51, 55, 59, 62, 66, 71, 75, 79, 84, 88, 93, 98, 103, 108, 113, 119, 124, 130, 136, 141, 147, 154, more...

integer, monotonic, +

a(n)=ceil(∑[n/8])
∑(a)=partial sums of a
n≥0
5 operations
Arithmetic

Sequence gjx0bxdrulpxl

0, 1, 1, 1, 2, 3, 3, 4, 6, 7, 8, 10, 12, 13, 15, 18, 20, 22, 25, 28, 30, 33, 37, 40, 43, 47, 51, 54, 58, 63, 67, 71, 76, 81, 85, 90, 96, 101, 106, 112, 118, 123, 129, 136, 142, 148, 155, 162, 168, 175, more...

integer, monotonic, +

a(n)=ceil(∑[n/7])
∑(a)=partial sums of a
n≥0
5 operations
Arithmetic

Sequence rdjpkeds4iy2j

0, 1, 1, 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 16, 18, 20, 23, 26, 29, 32, 35, 39, 43, 46, 50, 55, 59, 63, 68, 73, 78, 83, 88, 94, 100, 105, 111, 118, 124, 130, 137, 144, 151, 158, 165, 173, 181, 188, 196, 205, more...

integer, monotonic, +

a(n)=ceil(∑[n/6])
∑(a)=partial sums of a
n≥0
5 operations
Arithmetic

Sequence nmbue30rqmlkg

0, 1, 1, 2, 2, 3, 5, 6, 8, 9, 11, 14, 16, 19, 21, 24, 28, 31, 35, 38, 42, 47, 51, 56, 60, 65, 71, 76, 82, 87, 93, 100, 106, 113, 119, 126, 134, 141, 149, 156, 164, 173, 181, 190, 198, 207, 217, 226, 236, 245, more...

integer, monotonic, +

a(n)=ceil(∑[n/5])
∑(a)=partial sums of a
n≥0
5 operations
Arithmetic

Sequence pfkhbyqf0eodf

0, 1, 1, 2, 3, 4, 6, 7, 9, 12, 14, 17, 20, 23, 27, 30, 34, 39, 43, 48, 53, 58, 64, 69, 75, 82, 88, 95, 102, 109, 117, 124, 132, 141, 149, 158, 167, 176, 186, 195, 205, 216, 226, 237, 248, 259, 271, 282, 294, 307, more...

integer, monotonic, +

a(n)=ceil(∑[n/4])
∑(a)=partial sums of a
n≥0
5 operations
Arithmetic

Sequence s1wn0pi3girup

0, 1, 1, 2, 4, 5, 7, 10, 12, 15, 19, 22, 26, 31, 35, 40, 46, 51, 57, 64, 70, 77, 85, 92, 100, 109, 117, 126, 136, 145, 155, 166, 176, 187, 199, 210, 222, 235, 247, 260, 274, 287, 301, 316, 330, 345, 361, 376, 392, 409, more...

integer, monotonic, +

a(n)=ceil(∑[n/3])
∑(a)=partial sums of a
n≥0
5 operations
Arithmetic

Sequence xdlmgtmoqdwln

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, more...

integer, strictly-monotonic, +

a(n)=∑[ceil(n/10)]
∑(a)=partial sums of a
n≥0
5 operations
Arithmetic

Sequence chxqoycnh2ulb

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 141, 147, 153, 159, more...

integer, strictly-monotonic, +

a(n)=∑[ceil(n/9)]
∑(a)=partial sums of a
n≥0
5 operations
Arithmetic

Sequence qurezb5cyovpj

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 42, 45, 48, 52, 56, 60, 64, 68, 72, 76, 80, 85, 90, 95, 100, 105, 110, 115, 120, 126, 132, 138, 144, 150, 156, 162, 168, 175, more...

integer, strictly-monotonic, +

a(n)=∑[ceil(n/8)]
∑(a)=partial sums of a
n≥0
5 operations
Arithmetic

Sequence uzzi1nznhygdl

0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 17, 19, 21, 24, 27, 30, 33, 36, 39, 42, 46, 50, 54, 58, 62, 66, 70, 75, 80, 85, 90, 95, 100, 105, 111, 117, 123, 129, 135, 141, 147, 154, 161, 168, 175, 182, 189, 196, more...

integer, strictly-monotonic, +

a(n)=∑[ceil(n/7)]
∑(a)=partial sums of a
n≥0
5 operations
Arithmetic

Sequence sx1j2fpmmjlnk

0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 21, 24, 27, 30, 33, 36, 40, 44, 48, 52, 56, 60, 65, 70, 75, 80, 85, 90, 96, 102, 108, 114, 120, 126, 133, 140, 147, 154, 161, 168, 176, 184, 192, 200, 208, 216, 225, more...

integer, strictly-monotonic, +

a(n)=∑[ceil(n/6)]
∑(a)=partial sums of a
n≥0
5 operations
Arithmetic

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