Sequence Database

A database with 951925 machine generated integer and decimal sequences.

Displaying result 0-99 of total 271633. [0] [1] [2] [3] [4] ... [2716]

Sequence vtsqmvu022mjo

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, more...

integer, strictly-monotonic, +, A000217

a(n)=∑(n)
∑(a)=partial sums of a
n≥0
2 operations
Variable
a(n)=n+a(n-1)
a(0)=0
n≥0
3 operations
Recursive
a(n)=-∑(-n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=∑(gcd(n, n²))
gcd(a,b)=greatest common divisor
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑(sqrt(n*n))
∑(a)=partial sums of a
n≥0
5 operations
Power
a(n)=∑(C(n, a(n-1)))
a(0)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=∑(∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
4 operations
Prime

Sequence umplcbnlhplyn

0, -1, -3, -6, -10, -15, -21, -28, -36, -45, -55, -66, -78, -91, -105, -120, -136, -153, -171, -190, -210, -231, -253, -276, -300, -325, -351, -378, -406, -435, -465, -496, -528, -561, -595, -630, -666, -703, -741, -780, -820, -861, -903, -946, -990, -1035, -1081, -1128, -1176, -1225, more...

integer, strictly-monotonic, -

a(n)=a(n-1)-n
a(0)=0
n≥0
3 operations
Recursive
a(n)=∑(-n)
∑(a)=partial sums of a
n≥0
3 operations
Arithmetic
a(n)=a(n-1)^(2-1)-n
a(0)=0
n≥0
7 operations
Power
a(n)=-∑(C(n, a(n-1)))
a(0)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=a(n-1)-n%(1+n)
a(0)=0
n≥0
7 operations
Divisibility
a(n)=∑(-∑(agc(a(n-1))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence h3vrmorpscwhg

0, 1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, 819, 1015, 1240, 1496, 1785, 2109, 2470, 2870, 3311, 3795, 4324, 4900, 5525, 6201, 6930, 7714, 8555, 9455, 10416, 11440, 12529, 13685, 14910, 16206, 17575, 19019, 20540, 22140, 23821, 25585, 27434, 29370, 31395, 33511, 35720, 38024, 40425, more...

integer, strictly-monotonic, +, A000330

a(n)=∑(n²)
∑(a)=partial sums of a
n≥0
3 operations
Arithmetic
a(n)=n²+a(n-1)
a(0)=0
n≥0
4 operations
Recursive
a(n)=∑(lcm(n, n²))
lcm(a,b)=least common multiple
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=n^(1+1)+a(n-1)
a(0)=0
n≥0
7 operations
Power
a(n)=∑(∑(a(n-1)!)²)
a(0)=0
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑(∑(agc(a(n-1)))²)
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence rh2c2v1qn0g5g

0, 1, 9, 36, 100, 225, 441, 784, 1296, 2025, 3025, 4356, 6084, 8281, 11025, 14400, 18496, 23409, 29241, 36100, 44100, 53361, 64009, 76176, 90000, 105625, 123201, 142884, 164836, 189225, 216225, 246016, 278784, 314721, 354025, 396900, 443556, 494209, 549081, 608400, 672400, 741321, 815409, 894916, 980100, 1071225, 1168561, 1272384, 1382976, 1500625, more...

integer, strictly-monotonic, +, A000537

a(n)=∑(n)²
∑(a)=partial sums of a
n≥0
3 operations
Arithmetic
a(n)=∑(n^3)
∑(a)=partial sums of a
n≥0
4 operations
Power
a(n)=∑(1+a(n-1))²
a(0)=0
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑(C(n, a(n-1)))²
a(0)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑(∑(agc(a(n-1))))²
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence i41p5reh0akkh

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

integer, non-monotonic, +, A010052

a(n)=cf(n²)
cf(a)=characteristic function of a (in range)
n≥0
3 operations
Arithmetic
a(n)=cf(stern(n)²)
stern(n)=Stern-Brocot sequence
cf(a)=characteristic function of a (in range)
n≥0
4 operations
Recursive
a(n)=cf((n%8)²)
cf(a)=characteristic function of a (in range)
n≥0
5 operations
Divisibility
a(n)=sqrt(cf(n²))
cf(a)=characteristic function of a (in range)
n≥0
4 operations
Power
a(n)=cf(Δ(pt(n))²)
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
cf(a)=characteristic function of a (in range)
n≥0
5 operations
Combinatoric
a(n)=cf(Δ(τ(n))²)
τ(n)=number of divisors of n
Δ(a)=differences of a
cf(a)=characteristic function of a (in range)
n≥1
5 operations
Prime

Sequence 54zyjv03o4o0i

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, more...

integer, strictly-monotonic, +, A005408

a(n)=2+a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=Δ(n²)
Δ(a)=differences of a
n≥0
3 operations
Arithmetic
a(n)=∑(lcm(a(n-1), 2))
a(0)=1
lcm(a,b)=least common multiple
∑(a)=partial sums of a
n≥0
4 operations
Divisibility
a(n)=2^(2-1)+a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=∑(1+pt(a(n-1)))
a(0)=1
pt(n)=Pascals triangle by rows
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=∑(τ(1+a(n-1)))
a(0)=1
τ(n)=number of divisors of n
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence 4ocnuxty54zgg

2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, more...

integer, strictly-monotonic, +, A000037

a(n)=comp(n²)
comp(a)=complement function of a (in range)
n≥0
3 operations
Arithmetic
a(n)=comp(stern(n)²)
stern(n)=Stern-Brocot sequence
comp(a)=complement function of a (in range)
n≥0
4 operations
Recursive
a(n)=comp((n%8)²)
comp(a)=complement function of a (in range)
n≥0
5 operations
Divisibility
a(n)=comp(sqrt(n^4))
comp(a)=complement function of a (in range)
n≥0
5 operations
Power
a(n)=comp(Δ(pt(n))²)
pt(n)=Pascals triangle by rows
Δ(a)=differences of a
comp(a)=complement function of a (in range)
n≥0
5 operations
Combinatoric
a(n)=comp(∑(agc(a(n-1)))²)
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
comp(a)=complement function of a (in range)
n≥0
5 operations
Prime

Sequence dnb1wejvpehll

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)=n%2+a(n-1)
a(0)=0
n≥0
5 operations
Divisibility
a(n)=∑(sqrt(1-a(n-1)))
a(0)=0
∑(a)=partial sums of a
n≥0
5 operations
Power
a(n)=C(n-a(n-1), a(n-2))
a(0)=0
a(1)=1
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=∑(floor(cos(a(n-1))))
a(0)=0
∑(a)=partial sums of a
n≥0
4 operations
Trigonometric
a(n)=∑(Ω(2-a(n-1)))
a(0)=0
Ω(n)=max factorization terms
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence avvwp50xazwz

0, 1, 2, 2, 3, 4, 8, 3, 4, 12, 11, 6, 10, 19, 18, 4, 5, 24, 34, 11, 18, 24, 13, 14, 18, 39, 28, 20, 31, 46, 32, 5, 6, 40, 69, 36, 46, 33, 62, 20, 29, 66, 42, 37, 24, 38, 53, 22, 26, 89, more...

integer, non-monotonic, +

a(n)=stern(∑(n))
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
3 operations
Recursive
a(n)=stern(lcm(∑(n), 2))
∑(a)=partial sums of a
lcm(a,b)=least common multiple
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Divisibility
a(n)=stern(∑(C(n, a(n-1))))
a(0)=0
C(n,k)=binomial coefficient
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Combinatoric
a(n)=stern(∑(∑(agc(a(n-1)))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Prime

Sequence mrr5xzcftqxsg

0, 1, 2, 4, 5, 8, 10, 13, 14, 18, 21, 26, 28, 33, 36, 40, 41, 46, 50, 57, 60, 68, 73, 80, 82, 89, 94, 102, 105, 112, 116, 121, 122, 128, 133, 142, 146, 157, 164, 174, 177, 188, 196, 209, 214, 226, 233, 242, 244, 253, more...

integer, strictly-monotonic, +, A174868

a(n)=∑(stern(n))
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
3 operations
Recursive
a(n)=∑(stern(lcm(n, 2)))
lcm(a,b)=least common multiple
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=∑(stern(∑(a(n-1)!)))
a(0)=0
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Combinatoric
a(n)=∑(stern(∑(agc(a(n-1)))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
n≥0
5 operations
Prime

Sequence hndi1jkl020kk

1, 0, -2, -5, -9, -14, -20, -27, -35, -44, -54, -65, -77, -90, -104, -119, -135, -152, -170, -189, -209, -230, -252, -275, -299, -324, -350, -377, -405, -434, -464, -495, -527, -560, -594, -629, -665, -702, -740, -779, -819, -860, -902, -945, -989, -1034, -1080, -1127, -1175, -1224, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=1
n≥0
3 operations
Recursive
a(n)=1-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=a(n-1)^(2-1)-n
a(0)=1
n≥0
7 operations
Power
a(n)=a(n-1)-n%(1+n)
a(0)=1
n≥0
7 operations
Divisibility
a(n)=a(n-1)-∑(a(n-1)!)
a(0)=1
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=a(n-1)-∑(composite(a(n-1)))
a(0)=1
composite(n)=nth composite number
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence cy4jqnfcrgbrf

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

integer, non-monotonic, +-

a(n)=Δ(stern(n))
stern(n)=Stern-Brocot sequence
Δ(a)=differences of a
n≥0
3 operations
Recursive
a(n)=Δ(stern(lcm(n, 2)))
lcm(a,b)=least common multiple
stern(n)=Stern-Brocot sequence
Δ(a)=differences of a
n≥0
5 operations
Divisibility
a(n)=Δ(stern(∑(a(n-1)!)))
a(0)=0
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
Δ(a)=differences of a
n≥0
5 operations
Combinatoric
a(n)=Δ(stern(∑(agc(a(n-1)))))
a(0)=0
agc(n)=number of factorizations into prime powers (abelian group count)
∑(a)=partial sums of a
stern(n)=Stern-Brocot sequence
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence x1pra0juni4q

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

integer, periodic-2, non-monotonic, +, A059841

a(n)=1-a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=cf(2*n)
cf(a)=characteristic function of a (in range)
n≥0
4 operations
Arithmetic
a(n)=1-n%2
n≥0
5 operations
Divisibility
a(n)=a(n-2)^a(n-1)
a(0)=1
a(1)=0
n≥0
3 operations
Power
a(n)=floor(cos(a(n-1)))
a(0)=1
n≥0
3 operations
Trigonometric
a(n)=a(n-1)!-a(n-1)
a(0)=1
n≥0
4 operations
Combinatoric
a(n)=p(n+a(n-1))*a(n-2)/p(n)
a(0)=1
a(1)=0
p(n)=nth prime
n≥0
9 operations
Prime

Sequence mpt42acs3gazp

1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, 862, 904, 947, 991, 1036, 1082, 1129, 1177, 1226, more...

integer, strictly-monotonic, +, A000124

a(n)=n+a(n-1)
a(0)=1
n≥0
3 operations
Recursive
a(n)=1+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=∑(C(n, a(n-1)))
a(0)=1
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=n^(2-1)+a(n-1)
a(0)=1
n≥0
7 operations
Power
a(n)=n%(1+n)+a(n-1)
a(0)=1
n≥0
7 operations
Divisibility
a(n)=a(n-1)+∑(composite(a(n-1)))
a(0)=1
composite(n)=nth composite number
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence xbc4ucyt4ps4m

2, 1, -1, -4, -8, -13, -19, -26, -34, -43, -53, -64, -76, -89, -103, -118, -134, -151, -169, -188, -208, -229, -251, -274, -298, -323, -349, -376, -404, -433, -463, -494, -526, -559, -593, -628, -664, -701, -739, -778, -818, -859, -901, -944, -988, -1033, -1079, -1126, -1174, -1223, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=2
n≥0
3 operations
Recursive
a(n)=2-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=a(n-1)%(2*a(n-1))-n
a(0)=2
n≥0
7 operations
Divisibility

Sequence ul4ltexklmrij

2, 3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173, 192, 212, 233, 255, 278, 302, 327, 353, 380, 408, 437, 467, 498, 530, 563, 597, 632, 668, 705, 743, 782, 822, 863, 905, 948, 992, 1037, 1083, 1130, 1178, 1227, more...

integer, strictly-monotonic, +

a(n)=n+a(n-1)
a(0)=2
n≥0
3 operations
Recursive
a(n)=2+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n%a(n-1)+a(n-1)
a(0)=2
n≥0
5 operations
Divisibility
a(n)=∑(C(n, a(n-1)))
a(0)=2
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=∑(∑(μ(abs(a(n-1)))))
a(0)=2
μ(n)=Möbius function
∑(a)=partial sums of a
n≥0
5 operations
Prime

Sequence yw1uxhc1cwl5b

3, 2, 0, -3, -7, -12, -18, -25, -33, -42, -52, -63, -75, -88, -102, -117, -133, -150, -168, -187, -207, -228, -250, -273, -297, -322, -348, -375, -403, -432, -462, -493, -525, -558, -592, -627, -663, -700, -738, -777, -817, -858, -900, -943, -987, -1032, -1078, -1125, -1173, -1222, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=3
n≥0
3 operations
Recursive
a(n)=3-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence igwhwuompxban

3, 4, 6, 9, 13, 18, 24, 31, 39, 48, 58, 69, 81, 94, 108, 123, 139, 156, 174, 193, 213, 234, 256, 279, 303, 328, 354, 381, 409, 438, 468, 499, 531, 564, 598, 633, 669, 706, 744, 783, 823, 864, 906, 949, 993, 1038, 1084, 1131, 1179, 1228, more...

integer, strictly-monotonic, +, A152950

a(n)=n+a(n-1)
a(0)=3
n≥0
3 operations
Recursive
a(n)=3+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n%a(n-1)+a(n-1)
a(0)=3
n≥0
5 operations
Divisibility
a(n)=∑(C(n, a(n-1)))
a(0)=3
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=(n+a(n-1))%p(a(n-1))
a(0)=3
p(n)=nth prime
n≥0
6 operations
Prime

Sequence fydmgbr1xltee

4, 3, 1, -2, -6, -11, -17, -24, -32, -41, -51, -62, -74, -87, -101, -116, -132, -149, -167, -186, -206, -227, -249, -272, -296, -321, -347, -374, -402, -431, -461, -492, -524, -557, -591, -626, -662, -699, -737, -776, -816, -857, -899, -942, -986, -1031, -1077, -1124, -1172, -1221, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=4
n≥0
3 operations
Recursive
a(n)=4-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=(a(n-1)-n)%(n*a(n-1))
a(0)=4
n≥0
7 operations
Divisibility

Sequence rf05oegps3fwd

4, 5, 7, 10, 14, 19, 25, 32, 40, 49, 59, 70, 82, 95, 109, 124, 140, 157, 175, 194, 214, 235, 257, 280, 304, 329, 355, 382, 410, 439, 469, 500, 532, 565, 599, 634, 670, 707, 745, 784, 824, 865, 907, 950, 994, 1039, 1085, 1132, 1180, 1229, more...

integer, strictly-monotonic, +, A145018

a(n)=n+a(n-1)
a(0)=4
n≥0
3 operations
Recursive
a(n)=4+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n%a(n-1)+a(n-1)
a(0)=4
n≥0
5 operations
Divisibility
a(n)=∑(C(n, a(n-1)))
a(0)=4
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=(n+a(n-1))%p(a(n-1))
a(0)=4
p(n)=nth prime
n≥0
6 operations
Prime

Sequence 2trymnzjmmefh

5, 4, 2, -1, -5, -10, -16, -23, -31, -40, -50, -61, -73, -86, -100, -115, -131, -148, -166, -185, -205, -226, -248, -271, -295, -320, -346, -373, -401, -430, -460, -491, -523, -556, -590, -625, -661, -698, -736, -775, -815, -856, -898, -941, -985, -1030, -1076, -1123, -1171, -1220, more...

integer, strictly-monotonic, +-

a(n)=a(n-1)-n
a(0)=5
n≥0
3 operations
Recursive
a(n)=5-∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence spgub3wpte1il

5, 6, 8, 11, 15, 20, 26, 33, 41, 50, 60, 71, 83, 96, 110, 125, 141, 158, 176, 195, 215, 236, 258, 281, 305, 330, 356, 383, 411, 440, 470, 501, 533, 566, 600, 635, 671, 708, 746, 785, 825, 866, 908, 951, 995, 1040, 1086, 1133, 1181, 1230, more...

integer, strictly-monotonic, +

a(n)=n+a(n-1)
a(0)=5
n≥0
3 operations
Recursive
a(n)=5+∑(n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n%a(n-1)+a(n-1)
a(0)=5
n≥0
5 operations
Divisibility
a(n)=∑(C(n, a(n-1)))
a(0)=5
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
4 operations
Combinatoric
a(n)=(n+a(n-1))%p(a(n-1))
a(0)=5
p(n)=nth prime
n≥0
6 operations
Prime

Sequence asegayfwttyyd

-10, -19, -27, -34, -40, -45, -49, -52, -54, -55, -55, -54, -52, -49, -45, -40, -34, -27, -19, -10, 0, 11, 23, 36, 50, 65, 81, 98, 116, 135, 155, 176, 198, 221, 245, 270, 296, 323, 351, 380, 410, 441, 473, 506, 540, 575, 611, 648, 686, 725, more...

integer, non-monotonic, +-

a(n)=∑(n-10)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence g3oeqze35sqgm

-10, -9, -7, -4, 0, 5, 11, 18, 26, 35, 45, 56, 68, 81, 95, 110, 126, 143, 161, 180, 200, 221, 243, 266, 290, 315, 341, 368, 396, 425, 455, 486, 518, 551, 585, 620, 656, 693, 731, 770, 810, 851, 893, 936, 980, 1025, 1071, 1118, 1166, 1215, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-10
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence to010whxa40ak

-9, -17, -24, -30, -35, -39, -42, -44, -45, -45, -44, -42, -39, -35, -30, -24, -17, -9, 0, 10, 21, 33, 46, 60, 75, 91, 108, 126, 145, 165, 186, 208, 231, 255, 280, 306, 333, 361, 390, 420, 451, 483, 516, 550, 585, 621, 658, 696, 735, 775, more...

integer, non-monotonic, +-

a(n)=∑(n-9)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=∑(∑(a(n-1))-10)
a(0)=1
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence oj0ltlnkd0c2j

-9, -8, -6, -3, 1, 6, 12, 19, 27, 36, 46, 57, 69, 82, 96, 111, 127, 144, 162, 181, 201, 222, 244, 267, 291, 316, 342, 369, 397, 426, 456, 487, 519, 552, 586, 621, 657, 694, 732, 771, 811, 852, 894, 937, 981, 1026, 1072, 1119, 1167, 1216, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-9
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence t5z1cpf1nvbqi

-8, -15, -21, -26, -30, -33, -35, -36, -36, -35, -33, -30, -26, -21, -15, -8, 0, 9, 19, 30, 42, 55, 69, 84, 100, 117, 135, 154, 174, 195, 217, 240, 264, 289, 315, 342, 370, 399, 429, 460, 492, 525, 559, 594, 630, 667, 705, 744, 784, 825, more...

integer, non-monotonic, +-

a(n)=∑(n-8)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=∑(∑(a(n-1))-9)
a(0)=1
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence o2bpwxsqvzqmg

-8, -7, -5, -2, 2, 7, 13, 20, 28, 37, 47, 58, 70, 83, 97, 112, 128, 145, 163, 182, 202, 223, 245, 268, 292, 317, 343, 370, 398, 427, 457, 488, 520, 553, 587, 622, 658, 695, 733, 772, 812, 853, 895, 938, 982, 1027, 1073, 1120, 1168, 1217, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-8
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence qy4wnvnpgpbah

-7, -13, -18, -22, -25, -27, -28, -28, -27, -25, -22, -18, -13, -7, 0, 8, 17, 27, 38, 50, 63, 77, 92, 108, 125, 143, 162, 182, 203, 225, 248, 272, 297, 323, 350, 378, 407, 437, 468, 500, 533, 567, 602, 638, 675, 713, 752, 792, 833, 875, more...

integer, non-monotonic, +-

a(n)=∑(n-7)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=∑(∑(a(n-1))-8)
a(0)=1
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence lypqgpr01l13

-7, -6, -4, -1, 3, 8, 14, 21, 29, 38, 48, 59, 71, 84, 98, 113, 129, 146, 164, 183, 203, 224, 246, 269, 293, 318, 344, 371, 399, 428, 458, 489, 521, 554, 588, 623, 659, 696, 734, 773, 813, 854, 896, 939, 983, 1028, 1074, 1121, 1169, 1218, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-7
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence 4y1ctkcanpval

-6, -11, -15, -18, -20, -21, -21, -20, -18, -15, -11, -6, 0, 7, 15, 24, 34, 45, 57, 70, 84, 99, 115, 132, 150, 169, 189, 210, 232, 255, 279, 304, 330, 357, 385, 414, 444, 475, 507, 540, 574, 609, 645, 682, 720, 759, 799, 840, 882, 925, more...

integer, non-monotonic, +-

a(n)=∑(n-6)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=∑(∑(a(n-1))-7)
a(0)=1
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence gab4022npuc3k

-6, -5, -3, 0, 4, 9, 15, 22, 30, 39, 49, 60, 72, 85, 99, 114, 130, 147, 165, 184, 204, 225, 247, 270, 294, 319, 345, 372, 400, 429, 459, 490, 522, 555, 589, 624, 660, 697, 735, 774, 814, 855, 897, 940, 984, 1029, 1075, 1122, 1170, 1219, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-6
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence hsjs2pdiyk0dl

-5, -9, -12, -14, -15, -15, -14, -12, -9, -5, 0, 6, 13, 21, 30, 40, 51, 63, 76, 90, 105, 121, 138, 156, 175, 195, 216, 238, 261, 285, 310, 336, 363, 391, 420, 450, 481, 513, 546, 580, 615, 651, 688, 726, 765, 805, 846, 888, 931, 975, more...

integer, non-monotonic, +-

a(n)=∑(n-5)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=-∑(a(n-1)-1)
a(0)=5
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence gvwtlbs0hxihm

-5, -4, -2, 1, 5, 10, 16, 23, 31, 40, 50, 61, 73, 86, 100, 115, 131, 148, 166, 185, 205, 226, 248, 271, 295, 320, 346, 373, 401, 430, 460, 491, 523, 556, 590, 625, 661, 698, 736, 775, 815, 856, 898, 941, 985, 1030, 1076, 1123, 1171, 1220, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-5
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence kyl5y5xnisy4e

-5, -1.6666666667, -0.8333333333, -0.5, -0.3333333333, -0.2380952381, -0.1785714286, -0.1388888889, -0.1111111111, -0.0909090909, -0.0757575758, -0.0641025641, -0.0549450549, -0.0476190476, -0.0416666667, -0.0367647059, -0.0326797386, -0.0292397661, -0.0263157895, -0.0238095238, -0.0216450216, -0.0197628458, -0.018115942, -0.0166666667, -0.0153846154, more...

decimal, strictly-monotonic, -

a(n)=Δ(10/n)
Δ(a)=differences of a
n≥1
4 operations
Arithmetic
a(n)=Δ(10/∑(a(n-1)))
a(0)=1
∑(a)=partial sums of a
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence ba3fzg54evxsd

-4.5, -1.5, -0.75, -0.45, -0.3, -0.2142857143, -0.1607142857, -0.125, -0.1, -0.0818181818, -0.0681818182, -0.0576923077, -0.0494505495, -0.0428571429, -0.0375, -0.0330882353, -0.0294117647, -0.0263157895, -0.0236842105, -0.0214285714, -0.0194805195, -0.0177865613, -0.0163043478, -0.015, -0.0138461538, more...

decimal, strictly-monotonic, -

a(n)=Δ(9/n)
Δ(a)=differences of a
n≥1
4 operations
Arithmetic
a(n)=Δ(9/∑(a(n-1)))
a(0)=1
∑(a)=partial sums of a
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence fswqre0odq03m

-4, -7, -9, -10, -10, -9, -7, -4, 0, 5, 11, 18, 26, 35, 45, 56, 68, 81, 95, 110, 126, 143, 161, 180, 200, 221, 243, 266, 290, 315, 341, 368, 396, 425, 455, 486, 518, 551, 585, 620, 656, 693, 731, 770, 810, 851, 893, 936, 980, 1025, more...

integer, non-monotonic, +-

a(n)=∑(n-4)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=-∑(a(n-1)-1)
a(0)=4
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence wiz3nw2rzgc3e

-4, -3, -1, 2, 6, 11, 17, 24, 32, 41, 51, 62, 74, 87, 101, 116, 132, 149, 167, 186, 206, 227, 249, 272, 296, 321, 347, 374, 402, 431, 461, 492, 524, 557, 591, 626, 662, 699, 737, 776, 816, 857, 899, 942, 986, 1031, 1077, 1124, 1172, 1221, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-4
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence dxgjs1qtmdksi

-4, -1.3333333333, -0.6666666667, -0.4, -0.2666666667, -0.1904761905, -0.1428571429, -0.1111111111, -0.0888888889, -0.0727272727, -0.0606060606, -0.0512820513, -0.043956044, -0.0380952381, -0.0333333333, -0.0294117647, -0.0261437908, -0.0233918129, -0.0210526316, -0.019047619, -0.0173160173, -0.0158102767, -0.0144927536, -0.0133333333, -0.0123076923, more...

decimal, strictly-monotonic, -

a(n)=Δ(8/n)
Δ(a)=differences of a
n≥1
4 operations
Arithmetic
a(n)=Δ(8/∑(a(n-1)))
a(0)=1
∑(a)=partial sums of a
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence 5xvfp13xtqty

-3.5, -1.1666666667, -0.5833333333, -0.35, -0.2333333333, -0.1666666667, -0.125, -0.0972222222, -0.0777777778, -0.0636363636, -0.053030303, -0.0448717949, -0.0384615385, -0.0333333333, -0.0291666667, -0.0257352941, -0.022875817, -0.0204678363, -0.0184210526, -0.0166666667, -0.0151515152, -0.0138339921, -0.0126811594, -0.0116666667, -0.0107692308, more...

decimal, strictly-monotonic, -

a(n)=Δ(7/n)
Δ(a)=differences of a
n≥1
4 operations
Arithmetic
a(n)=Δ(7/∑(a(n-1)))
a(0)=1
∑(a)=partial sums of a
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence vxst0i323go3o

-3.1415926536, -5.2831853072, -6.4247779608, -6.5663706144, -5.7079632679, -3.8495559215, -0.9911485751, 2.8672587713, 7.7256661177, 13.5840734641, 20.4424808105, 28.3008881569, 37.1592955033, 47.0177028497, 57.8761101962, 69.7345175426, 82.592924889, 96.4513322354, 111.3097395818, 127.1681469282, 144.0265542746, 161.884961621, 180.7433689674, 200.6017763138, 221.4601836603, more...

decimal, non-monotonic, +-

a(n)=∑(n-π)
π=3.141...
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence 1gux1013g4cvc

-3.1415926536, -2.1415926536, -0.1415926536, 2.8584073464, 6.8584073464, 11.8584073464, 17.8584073464, 24.8584073464, 32.8584073464, 41.8584073464, 51.8584073464, 62.8584073464, 74.8584073464, 87.8584073464, 101.8584073464, 116.8584073464, 132.8584073464, 149.8584073464, 167.8584073464, 186.8584073464, 206.8584073464, 227.8584073464, 249.8584073464, 272.8584073464, 296.8584073464, more...

decimal, strictly-monotonic, +-

a(n)=∑(n)-π
∑(a)=partial sums of a
π=3.141...
n≥0
4 operations
Arithmetic

Sequence p2t33hwohlwkk

-3.1415926536, 6.7280117475, -7.6806487842, 1.0875234426, 0.9335381126, 1.7348940865, 4.9590340022, 19.1339732252, 92.9606360834, 544.601273358, 3735.0973740628, 29351.9166438926, 260011.2340294778, 2563296.659705388, 27833319.28077373, 330058837.83410805, 4244030985.1537104, 58815510183.04673, more...

decimal, non-monotonic, +-

a(n)=∏(n-π)
π=3.141...
∏(a)=partial products of a
n≥0
4 operations
Arithmetic

Sequence uekrfj3vojcy

-3, -5, -6, -6, -5, -3, 0, 4, 9, 15, 22, 30, 39, 49, 60, 72, 85, 99, 114, 130, 147, 165, 184, 204, 225, 247, 270, 294, 319, 345, 372, 400, 429, 459, 490, 522, 555, 589, 624, 660, 697, 735, 774, 814, 855, 897, 940, 984, 1029, 1075, more...

integer, non-monotonic, +-

a(n)=∑(n-3)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=-∑(a(n-1)-1)
a(0)=3
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence e0tgg14pfiwmp

-3, -2, 0, 3, 7, 12, 18, 25, 33, 42, 52, 63, 75, 88, 102, 117, 133, 150, 168, 187, 207, 228, 250, 273, 297, 322, 348, 375, 403, 432, 462, 493, 525, 558, 592, 627, 663, 700, 738, 777, 817, 858, 900, 943, 987, 1032, 1078, 1125, 1173, 1222, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-3
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence eomzduuesj3yc

-3, -1, -0.5, -0.3, -0.2, -0.1428571429, -0.1071428571, -0.0833333333, -0.0666666667, -0.0545454545, -0.0454545455, -0.0384615385, -0.032967033, -0.0285714286, -0.025, -0.0220588235, -0.0196078431, -0.0175438596, -0.0157894737, -0.0142857143, -0.012987013, -0.0118577075, -0.0108695652, -0.01, -0.0092307692, more...

decimal, strictly-monotonic, -

a(n)=Δ(6/n)
Δ(a)=differences of a
n≥1
4 operations
Arithmetic
a(n)=Δ(6/∑(a(n-1)))
a(0)=1
∑(a)=partial sums of a
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence pq1bhqoktlrbn

-2.5, -0.8333333333, -0.4166666667, -0.25, -0.1666666667, -0.119047619, -0.0892857143, -0.0694444444, -0.0555555556, -0.0454545455, -0.0378787879, -0.0320512821, -0.0274725275, -0.0238095238, -0.0208333333, -0.0183823529, -0.0163398693, -0.014619883, -0.0131578947, -0.0119047619, -0.0108225108, -0.0098814229, -0.009057971, -0.0083333333, -0.0076923077, more...

decimal, strictly-monotonic, -

a(n)=Δ(5/n)
Δ(a)=differences of a
n≥1
4 operations
Arithmetic
a(n)=Δ(5/∑(a(n-1)))
a(0)=1
∑(a)=partial sums of a
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence kb3orp4c405sn

-2, -3, -3, -2, 0, 3, 7, 12, 18, 25, 33, 42, 52, 63, 75, 88, 102, 117, 133, 150, 168, 187, 207, 228, 250, 273, 297, 322, 348, 375, 403, 432, 462, 493, 525, 558, 592, 627, 663, 700, 738, 777, 817, 858, 900, 943, 987, 1032, 1078, 1125, more...

integer, non-monotonic, +-, A167544

a(n)=∑(n-2)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=-∑(a(n-1)-1)
a(0)=2
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence v3vkuw40xipti

-2, -1, 1, 4, 8, 13, 19, 26, 34, 43, 53, 64, 76, 89, 103, 118, 134, 151, 169, 188, 208, 229, 251, 274, 298, 323, 349, 376, 404, 433, 463, 494, 526, 559, 593, 628, 664, 701, 739, 778, 818, 859, 901, 944, 988, 1033, 1079, 1126, 1174, 1223, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-2
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence jeyzgqxo0rkjp

-2, -0.6666666667, -0.3333333333, -0.2, -0.1333333333, -0.0952380952, -0.0714285714, -0.0555555556, -0.0444444444, -0.0363636364, -0.0303030303, -0.0256410256, -0.021978022, -0.019047619, -0.0166666667, -0.0147058824, -0.0130718954, -0.0116959064, -0.0105263158, -0.0095238095, -0.0086580087, -0.0079051383, -0.0072463768, -0.0066666667, -0.0061538462, more...

decimal, strictly-monotonic, -

a(n)=Δ(4/n)
Δ(a)=differences of a
n≥1
4 operations
Arithmetic
a(n)=Δ(4/∑(a(n-1)))
a(0)=1
∑(a)=partial sums of a
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence gioe1hte0yd4l

-1.5707963268, -0.5235987756, -0.2617993878, -0.1570796327, -0.1047197551, -0.0747998251, -0.0560998688, -0.0436332313, -0.034906585, -0.0285599332, -0.0237999443, -0.0201384144, -0.0172614981, -0.014959965, -0.0130899694, -0.011549973, -0.0102666427, -0.0091859434, -0.0082673491, -0.0074799825, -0.0067999841, -0.0062086811, -0.005691291, -0.0052359878, -0.0048332195, more...

decimal, strictly-monotonic, -

a(n)=Δ(π/n)
π=3.141...
Δ(a)=differences of a
n≥1
4 operations
Arithmetic
a(n)=Δ(π/∑(a(n-1)))
a(0)=1
π=3.141...
∑(a)=partial sums of a
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence 5tvgwvq1zsldj

-1.5, -0.5, -0.25, -0.15, -0.1, -0.0714285714, -0.0535714286, -0.0416666667, -0.0333333333, -0.0272727273, -0.0227272727, -0.0192307692, -0.0164835165, -0.0142857143, -0.0125, -0.0110294118, -0.0098039216, -0.0087719298, -0.0078947368, -0.0071428571, -0.0064935065, -0.0059288538, -0.0054347826, -0.005, -0.0046153846, more...

decimal, strictly-monotonic, -

a(n)=Δ(3/n)
Δ(a)=differences of a
n≥1
4 operations
Arithmetic
a(n)=Δ(3/∑(a(n-1)))
a(0)=1
∑(a)=partial sums of a
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence ral3ikpq5phon

-1, -1, 0, 2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90, 104, 119, 135, 152, 170, 189, 209, 230, 252, 275, 299, 324, 350, 377, 405, 434, 464, 495, 527, 560, 594, 629, 665, 702, 740, 779, 819, 860, 902, 945, 989, 1034, 1080, 1127, 1175, more...

integer, monotonic, +-

a(n)=∑(n-1)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=-∑(a(n-1)-1)
a(0)=1
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence kbt4jgby1ufie

-1, -0.3333333333, -0.1666666667, -0.1, -0.0666666667, -0.0476190476, -0.0357142857, -0.0277777778, -0.0222222222, -0.0181818182, -0.0151515152, -0.0128205128, -0.010989011, -0.0095238095, -0.0083333333, -0.0073529412, -0.0065359477, -0.0058479532, -0.0052631579, -0.0047619048, -0.0043290043, -0.0039525692, -0.0036231884, -0.0033333333, -0.0030769231, more...

decimal, strictly-monotonic, -

a(n)=Δ(2/n)
Δ(a)=differences of a
n≥1
4 operations
Arithmetic
a(n)=Δ(2/∑(a(n-1)))
a(0)=1
∑(a)=partial sums of a
Δ(a)=differences of a
n≥0
5 operations
Recursive

Sequence ahcpequn050lm

-1, 0, 2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90, 104, 119, 135, 152, 170, 189, 209, 230, 252, 275, 299, 324, 350, 377, 405, 434, 464, 495, 527, 560, 594, 629, 665, 702, 740, 779, 819, 860, 902, 945, 989, 1034, 1080, 1127, 1175, 1224, more...

integer, strictly-monotonic, +-

a(n)=∑(n)-1
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence 3u4ibfcgpvbpm

-0.5, -0.1666666667, -0.0833333333, -0.05, -0.0333333333, -0.0238095238, -0.0178571429, -0.0138888889, -0.0111111111, -0.0090909091, -0.0075757576, -0.0064102564, -0.0054945055, -0.0047619048, -0.0041666667, -0.0036764706, -0.0032679739, -0.0029239766, -0.0026315789, -0.0023809524, -0.0021645022, -0.0019762846, -0.0018115942, -0.0016666667, -0.0015384615, more...

decimal, strictly-monotonic, -

a(n)=Δ(1/n)
Δ(a)=differences of a
n≥1
4 operations
Arithmetic
a(n)=Δ(1/∑(a(n-1)))
a(0)=1
∑(a)=partial sums of a
Δ(a)=differences of a
n≥0
5 operations
Recursive
a(n)=Δ(n^-1)
Δ(a)=differences of a
n≥1
5 operations
Power

Sequence ijoirlgtl1rj

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

Sequence osupob4yuo4ql

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

Sequence j5p1mjiwf0ylg

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

Sequence vfodn4rv1ejnp

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 1csiyc0a2fqs

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 qi5vvf5c1dr5p

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)=∑(cf(10+a(n-1)))
a(0)=5
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence przvrdkclisad

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)=∑(cf(9+a(n-1)))
a(0)=5
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence uziproz30uome

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)=∑(cf(5+a(n-1)))
a(0)=5
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑(sqrt(cf(∑(a(n-1)))))
a(0)=5
∑(a)=partial sums of a
cf(a)=characteristic function of a (in range)
n≥0
5 operations
Power
a(n)=∑(cf(∑(gpf(a(n-1)))))
a(0)=5
gpf(n)=greatest prime factor of n
∑(a)=partial sums of a
cf(a)=characteristic function of a (in range)
n≥0
5 operations
Prime

Sequence pqy5fian4wqyp

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)=∑(cf(8+a(n-1)))
a(0)=4
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence q10tkieof21od

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)=∑(cf(7+a(n-1)))
a(0)=4
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence qxajx0kofi1me

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)=∑(cf(4+a(n-1)))
a(0)=4
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑(sqrt(cf(∑(a(n-1)))))
a(0)=4
∑(a)=partial sums of a
cf(a)=characteristic function of a (in range)
n≥0
5 operations
Power

Sequence e0qiz3vtfm1cc

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=3.141...
n≥0
4 operations
Arithmetic

Sequence 3kbd0f35vzbzo

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)=∑(cf(6+a(n-1)))
a(0)=3
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence f1vfeuovfrvgl

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)=∑(cf(5+a(n-1)))
a(0)=3
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence g1oapuftv2mm

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)=∑(cf(3+a(n-1)))
a(0)=3
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive
a(n)=∑(sqrt(cf(∑(a(n-1)))))
a(0)=3
∑(a)=partial sums of a
cf(a)=characteristic function of a (in range)
n≥0
5 operations
Power
a(n)=∑(cf(∑(P(a(n-1)))))
a(0)=3
P(n)=Partition numbers
∑(a)=partial sums of a
cf(a)=characteristic function of a (in range)
n≥0
5 operations
Combinatoric
a(n)=∑(cf(∑(gpf(a(n-1)))))
a(0)=3
gpf(n)=greatest prime factor of n
∑(a)=partial sums of a
cf(a)=characteristic function of a (in range)
n≥0
5 operations
Prime

Sequence pxu5roftflxj

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)=∑(cf(4+a(n-1)))
a(0)=2
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence sgta3ppmvzlyg

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=3.141...
n≥0
4 operations
Arithmetic

Sequence steuesysupkad

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)=∑(a(n-3))-a(n-1)
a(0)=0
a(1)=1
a(2)=1
∑(a)=partial sums of a
n≥0
4 operations
Recursive
a(n)=C(a(n-1), n)+a(n-3)
a(0)=0
a(1)=0
a(2)=1
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
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
Power
a(n)=λ(a(n-1)²)+a(n-3)
a(0)=0
a(1)=0
a(2)=1
λ(n)=Liouville's function
n≥0
5 operations
Prime
a(n)=gcd(∑(a(n-1)), ∑(a(n-3)))
a(0)=0
a(1)=0
a(2)=1
∑(a)=partial sums of a
gcd(a,b)=greatest common divisor
n≥0
5 operations
Divisibility

Sequence rqs0vzragjdkn

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)=n-1-a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=(n-n%2)/2
n≥0
7 operations
Divisibility
a(n)=C(a(n-1), n)+a(n-2)
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
4 operations
Power
a(n)=agc(∑(a(n-1)))+a(n-2)
a(0)=0
a(1)=0
∑(a)=partial sums of a
agc(n)=number of factorizations into prime powers (abelian group count)
n≥0
5 operations
Prime

Sequence 0r02t3allbm1c

0, 0.1, 0.3, 0.6, 1, 1.5, 2.1, 2.8, 3.6, 4.5, 5.5, 6.6, 7.8, 9.1, 10.5, 12, 13.6, 15.3, 17.1, 19, 21, 23.1, 25.3, 27.6, 30, more...

decimal, strictly-monotonic, +

a(n)=n/10+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/10)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence zuk4mafgnyckn

0, 0.1111111111, 0.3333333333, 0.6666666667, 1.1111111111, 1.6666666667, 2.3333333333, 3.1111111111, 4, 5, 6.1111111111, 7.3333333333, 8.6666666667, 10.1111111111, 11.6666666667, 13.3333333333, 15.1111111111, 17, 19, 21.1111111111, 23.3333333333, 25.6666666667, 28.1111111111, 30.6666666667, 33.3333333333, more...

decimal, strictly-monotonic, +

a(n)=n/9+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/9)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence vwe1giakvordj

0, 0.125, 0.375, 0.75, 1.25, 1.875, 2.625, 3.5, 4.5, 5.625, 6.875, 8.25, 9.75, 11.375, 13.125, 15, 17, 19.125, 21.375, 23.75, 26.25, 28.875, 31.625, 34.5, 37.5, more...

decimal, strictly-monotonic, +

a(n)=n/8+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/8)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence vkopigykd5nqf

0, 0.1428571429, 0.4285714286, 0.8571428571, 1.4285714286, 2.1428571429, 3, 4, 5.1428571429, 6.4285714286, 7.8571428571, 9.4285714286, 11.1428571429, 13, 15, 17.1428571429, 19.4285714286, 21.8571428571, 24.4285714286, 27.1428571429, 30, 33, 36.1428571429, 39.4285714286, 42.8571428571, more...

decimal, strictly-monotonic, +

a(n)=n/7+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/7)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence w4zy1aju55stc

0, 0.1666666667, 0.5, 1, 1.6666666667, 2.5, 3.5, 4.6666666667, 6, 7.5, 9.1666666667, 11, 13, 15.1666666667, 17.5, 20, 22.6666666667, 25.5, 28.5, 31.6666666667, 35, 38.5, 42.1666666667, 46, 50, more...

decimal, strictly-monotonic, +

a(n)=n/6+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/6)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence h143rak2gl0ce

0, 0.2, 0.6, 1.2, 2, 3, 4.2, 5.6, 7.2, 9, 11, 13.2, 15.6, 18.2, 21, 24, 27.2, 30.6, 34.2, 38, 42, 46.2, 50.6, 55.2, 60, more...

decimal, strictly-monotonic, +

a(n)=n/5+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/5)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence shwvfna0ogvd

0, 0.25, 0.75, 1.5, 2.5, 3.75, 5.25, 7, 9, 11.25, 13.75, 16.5, 19.5, 22.75, 26.25, 30, 34, 38.25, 42.75, 47.5, 52.5, 57.75, 63.25, 69, 75, more...

decimal, strictly-monotonic, +

a(n)=n/4+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/4)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence tajclfbi5desj

0, 0.3183098862, 0.9549296586, 1.9098593171, 3.1830988618, 4.7746482928, 6.6845076099, 8.9126768131, 11.4591559026, 14.3239448783, 17.5070437401, 21.0084524881, 24.8281711223, 28.9661996427, 33.4225380493, 38.1971863421, 43.290144521, 48.7014125861, 54.4309905374, 60.4788783749, 66.8450760986, 73.5295837085, 80.5324012045, 87.8535285867, 95.4929658551, more...

decimal, strictly-monotonic, +

a(n)=n/π+a(n-1)
a(0)=0
π=3.141...
n≥0
5 operations
Recursive
a(n)=∑(n/π)
π=3.141...
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence exxcim4pcj3vj

0, 0.3333333333, 1, 2, 3.3333333333, 5, 7, 9.3333333333, 12, 15, 18.3333333333, 22, 26, 30.3333333333, 35, 40, 45.3333333333, 51, 57, 63.3333333333, 70, 77, 84.3333333333, 92, 100, more...

decimal, strictly-monotonic, +

a(n)=n/3+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(n/3)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence z2mb2oag0by5b

0, 0.5, 1.5, 3, 5, 7.5, 10.5, 14, 18, 22.5, 27.5, 33, 39, 45.5, 52.5, 60, 68, 76.5, 85.5, 95, 105, 115.5, 126.5, 138, 150, more...

decimal, strictly-monotonic, +

a(n)=∑(n/2)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=n/2+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(log(sqrt(exp(n))))
∑(a)=partial sums of a
n≥0
5 operations
Power

Sequence donwd0iifx2ao

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)=∑(cf(10+a(n-1)))
a(0)=1
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence z4fe1xb4bugag

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)=∑(cf(9+a(n-1)))
a(0)=1
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence d1310nsmujg3m

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)=∑(cf(8+a(n-1)))
a(0)=1
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence uasmztrrr05hp

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)=∑(cf(7+a(n-1)))
a(0)=1
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence x0o5lzir3u2gh

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)=∑(cf(6+a(n-1)))
a(0)=1
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence sk0o4ecibriyb

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)=∑(cf(5+a(n-1)))
a(0)=1
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence 14ulug4m45x4f

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)=∑(cf(4+a(n-1)))
a(0)=1
cf(a)=characteristic function of a (in range)
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence tfj5jo3om1nfe

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=3.141...
n≥0
4 operations
Arithmetic

Sequence 0wrezc013drpf

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)=n-a(n-1)-a(n-2)
a(0)=0
a(1)=1
n≥0
5 operations
Recursive
a(n)=C(a(n-1), n)+a(n-3)
a(0)=0
a(1)=1
a(2)=1
C(n,k)=binomial coefficient
n≥0
5 operations
Combinatoric
a(n)=exp(∑(a(n-1)))+a(n-3)
a(0)=0
a(1)=1
a(2)=1
∑(a)=partial sums of a
n≥0
5 operations
Power
a(n)=λ(a(n-1)²)+a(n-3)
a(0)=0
a(1)=1
a(2)=1
λ(n)=Liouville's function
n≥0
5 operations
Prime
a(n)=(n+a(n-1))%2+a(n-2)
a(0)=0
a(1)=1
n≥0
7 operations
Divisibility

Sequence aowqxobot5eib

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(π*n)
π=3.141...
n≥0
4 operations
Arithmetic

Sequence ewfvehr3q41zj

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(π*n)
π=3.141...
n≥0
4 operations
Arithmetic

Sequence hkdawpl1vmhoe

0, 3, 9, 18, 30, 45, 63, 84, 108, 135, 165, 198, 234, 273, 315, 360, 408, 459, 513, 570, 630, 693, 759, 828, 900, 975, 1053, 1134, 1218, 1305, 1395, 1488, 1584, 1683, 1785, 1890, 1998, 2109, 2223, 2340, 2460, 2583, 2709, 2838, 2970, 3105, 3243, 3384, 3528, 3675, more...

integer, strictly-monotonic, +, A045943

a(n)=∑(3*n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=3*n+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(∑(gcd(a(n-1), 3)))
a(0)=0
gcd(a,b)=greatest common divisor
∑(a)=partial sums of a
n≥0
5 operations
Divisibility

Sequence 4q5f155ooprpg

0, 3.1415926536, 9.4247779608, 18.8495559215, 31.4159265359, 47.1238898038, 65.9734457254, 87.9645943005, 113.0973355292, 141.3716694115, 172.7875959474, 207.3451151369, 245.04422698, 285.8849314767, 329.8672286269, 376.9911184308, 427.2566008882, 480.6636759992, 537.2123437639, 596.9026041821, 659.7344572539, 725.7079029792, 794.8229413582, 867.0795723908, 942.4777960769, more...

decimal, strictly-monotonic, +

a(n)=π*n+a(n-1)
a(0)=0
π=3.141...
n≥0
5 operations
Recursive
a(n)=∑(π*n)
π=3.141...
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic

Sequence xrxgobxx3pzhe

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(π*n)
π=3.141...
n≥0
4 operations
Arithmetic

Sequence ysvzf1qoeah4l

0, 4, 12, 24, 40, 60, 84, 112, 144, 180, 220, 264, 312, 364, 420, 480, 544, 612, 684, 760, 840, 924, 1012, 1104, 1200, 1300, 1404, 1512, 1624, 1740, 1860, 1984, 2112, 2244, 2380, 2520, 2664, 2812, 2964, 3120, 3280, 3444, 3612, 3784, 3960, 4140, 4324, 4512, 4704, 4900, more...

integer, strictly-monotonic, +, A046092

a(n)=∑(4*n)
∑(a)=partial sums of a
n≥0
4 operations
Arithmetic
a(n)=4*n+a(n-1)
a(0)=0
n≥0
5 operations
Recursive
a(n)=∑(∑(gcd(a(n-1), 4)))
a(0)=0
gcd(a,b)=greatest common divisor
∑(a)=partial sums of a
n≥0
5 operations
Divisibility
a(n)=n*∑(a(n-1)!)
a(0)=2
∑(a)=partial sums of a
n≥0
5 operations
Combinatoric
a(n)=n*∑(τ(a(n-1)))
a(0)=2
τ(n)=number of divisors of n
∑(a)=partial sums of a
n≥0
5 operations
Prime

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