Sequence Database

A database with 2076264 machine generated integer and decimal sequences.

Found 16 matches.

Sequence hwca0hh1eg2yn

1, 3, 6, 9, 13, 17, 21, 26, 33, 40, 48, 56, 64, 73, 85, 95, 107, 121, 134, 151, 170, 190, 210, 232, 257, 284, 314, 343, 377, 412, 450, 491, 537, 582, 635, 694, 750, 806, 868, 929, 994, 1063, 1138, 1221, 1309, 1389, 1475, 1576, 1675, 1777, more...

integer, strictly-monotonic, +

a(n)=∑[stern(a(n-1))+a(n-3)]
a(0)=1
a(1)=2
a(2)=3
stern(n)=Stern-Brocot sequence
∑(a)=partial sums of a
n≥0
5 operations
Recursive

Sequence gwlvmljltlyap

5, 6, 8, 11, 13, 17, 21, 26, 32, 39, 48, 57, 68, 81, 97, 114, 134, 156, 182, 210, 243, 281, 321, 369, 423, 480, 548, 619, 699, 789, 892, 1003, 1127, 1268, 1409, 1581, 1761, 1966, 2179, 2431, 2705, 2992, 3305, 3665, 4050, 4478, 4924, 5426, 5982, 6566, more...

integer, strictly-monotonic, +

a(n)=2+Δ[composite(a(n-1))]
a(0)=3
composite(n)=nth composite number
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence hheeisdunllci

6, 8, 11, 13, 17, 21, 26, 32, 39, 48, 57, 68, 81, 97, 113, 134, 156, 182, 210, 243, 281, 321, 369, 423, 479, 548, 619, 699, 788, 892, 1002, 1127, 1267, 1409, 1581, 1760, 1964, 2178, 2431, 2703, 2991, 3304, 3664, 4047, 4478, 4922, 5423, 5980, 6562, 7206, more...

integer, strictly-monotonic, +

a(n)=2+Δ[composite(a(n-1))]
a(0)=5
composite(n)=nth composite number
Δ(a)=differences of a
n≥0
5 operations
Prime

Sequence cqfz24akm2m2j

0, 1, 2, 4, 7, 8, 12, 17, 21, 26, 34, 43, 48, 57, 64, 71, 75, 82, 101, 113, 123, 128, 136, 155, 165, 184, 207, 212, 246, 265, 282, 317, 333, 360, 403, 422, 466, 509, 517, 532, 577, 600, 661, 710, 766, 783, 792, 847, 860, 926, more...

integer, strictly-monotonic, +

a(n)=stern(1+a(n-1))+a(n-1)
a(0)=0
stern(n)=Stern-Brocot sequence
n≥0
6 operations
Recursive

Sequence soep2c5v5v5vn

1, 1, 1, 2, 3, 4, 6, 8, 11, 14, 17, 21, 26, 32, 39, 46, 55, 65, 76, 88, 102, 118, 136, 156, 177, 201, 228, 257, 289, 325, 363, 405, 451, 501, 555, 614, 678, 746, 821, 901, 987, 1080, 1180, 1286, 1401, 1524, 1655, 1795, 1945, 2104, more...

integer, monotonic, +

a(n)=floor(n^log(sqrt(n)))
n≥1
6 operations
Power

Sequence 512tpqdq4aprj

1, 1, 2, 6, 8, 11, 17, 21, 26, 34, 40, 47, 57, 65, 74, 86, 96, 107, 121, 133, 146, 162, 176, 191, 209, 225, 242, 262, 280, 299, 321, 341, 362, 386, 408, 431, 457, 481, 506, 534, 560, 587, 617, 645, 674, 706, 736, 767, 801, 833, more...

integer, monotonic, +

a(n)=n²-a(n-1)-a(n-2)
a(0)=1
a(1)=1
n≥0
6 operations
Recursive

Sequence nfaiyndbhelpj

1, 2, 4, 7, 8, 12, 17, 21, 26, 34, 43, 48, 57, 64, 71, 75, 82, 101, 113, 123, 128, 136, 155, 165, 184, 207, 212, 246, 265, 282, 317, 333, 360, 403, 422, 466, 509, 517, 532, 577, 600, 661, 710, 766, 783, 792, 847, 860, 926, 964, more...

integer, strictly-monotonic, +

a(n)=stern(1+a(n-1))+a(n-1)
a(0)=1
stern(n)=Stern-Brocot sequence
n≥0
6 operations
Recursive

Sequence a40rsiakq4j4p

1, 2, 5, 6, 11, 11, 12, 14, 17, 21, 26, 32, 39, 47, 56, 66, 77, 89, 102, 116, 131, 147, 164, 182, 201, 221, 242, 264, 287, 311, 336, 362, 389, 417, 446, 476, 507, 539, 572, 606, 641, 677, 714, 752, 791, 831, 872, 914, 957, 1001, more...

integer, monotonic, +

a(n)=∑[C(2+a(n-2), a(n-1))]
a(0)=1
a(1)=1
C(n,k)=binomial coefficient
∑(a)=partial sums of a
n≥0
6 operations
Combinatoric

Sequence 1vzqe03sh0wec

1, 2, 6, 8, 11, 17, 21, 26, 34, 40, 47, 57, 65, 74, 86, 96, 107, 121, 133, 146, 162, 176, 191, 209, 225, 242, 262, 280, 299, 321, 341, 362, 386, 408, 431, 457, 481, 506, 534, 560, 587, 617, 645, 674, 706, 736, 767, 801, 833, 866, more...

integer, strictly-monotonic, +, A130205

a(n)=n²-a(n-1)-a(n-2)
a(0)=1
a(1)=2
n≥1
6 operations
Recursive
a(n)=∑[4-pt(9+a(n-1))]+a(n-1)
a(0)=1
pt(n)=Pascals triangle by rows
∑(a)=partial sums of a
n≥0
9 operations
Combinatoric

Sequence oijb3lhggqndd

2, 4, 7, 8, 12, 17, 21, 26, 34, 43, 48, 57, 64, 71, 75, 82, 101, 113, 123, 128, 136, 155, 165, 184, 207, 212, 246, 265, 282, 317, 333, 360, 403, 422, 466, 509, 517, 532, 577, 600, 661, 710, 766, 783, 792, 847, 860, 926, 964, 1011, more...

integer, strictly-monotonic, +

a(n)=stern(1+a(n-1))+a(n-1)
a(0)=2
stern(n)=Stern-Brocot sequence
n≥0
6 operations
Recursive

Sequence 2hlx3yxa32dwb

1, 2, 3, 4, 5, 6, 8, 10, 13, 17, 21, 26, 32, 39, 47, 56, 67, 79, 92, 107, 123, 141, 161, 183, 207, 232, 260, 290, 322, 356, 392, 431, 472, 516, 563, 612, 664, 719, 777, 838, 902, 970, 1041, 1115, 1193, 1274, 1359, 1448, 1541, 1638, more...

integer, strictly-monotonic, +, A054961 (multiple)

a(n)=ceil((n/5)²)+a(n-1)
a(0)=1
n≥0
7 operations
Recursive
a(n)=1+∑[ceil((n/5)²)]
∑(a)=partial sums of a
n≥0
8 operations
Power

Sequence 203l2sqwtvmah

2, 3.5, 5.666666666666667, 8.5, 12, 16.166666666666664, 21, 26.5, 32.66666666666667, 39.5, 47, 55.166666666666664, 64, 73.5, 83.66666666666667, 94.5, 106, 118.16666666666667, 131, 144.5, 158.66666666666666, 173.5, 189, 205.16666666666666, 222, more...

decimal, strictly-monotonic, +

a(n)=1+∑[n²]/n
∑(a)=partial sums of a
n≥1
7 operations
Power

Sequence ulz2f0eraukic

2, 3.5, 5.666666666666667, 8.5, 12, 16.166666666666668, 21, 26.5, 32.666666666666664, 39.5, 47, 55.166666666666664, 64, 73.5, 83.66666666666667, 94.5, 106, 118.16666666666667, 131, 144.5, 158.66666666666666, 173.5, 189, 205.16666666666666, 222, more...

decimal, strictly-monotonic, +

a(n)=∑[1+n²]/n
∑(a)=partial sums of a
n≥1
7 operations
Power

Sequence ds2fikzf3aioo

0, 1, 0, 3, 6, 7, 12, 17, 20, 27, 34, 39, 48, 57, 64, 75, 86, 95, 108, 121, 132, 147, 162, 175, 192, 209, 224, 243, 262, 279, 300, 321, 340, 363, 386, 407, 432, 457, 480, 507, 534, 559, 588, 617, 644, 675, 706, 735, 768, 801, more...

integer, non-monotonic, +

a(n)=(1-n)²-a(n-1)-a(n-2)
a(0)=0
a(1)=1
n≥0
8 operations
Recursive

Sequence za1iktfn3lbxh

1, 1, 2, 4, 8, 13, 13, 15, 17, 20, 25, 32, 39, 46, 55, 66, 79, 95, 95, 115, 117, 118, 120, 123, 125, 127, 130, 134, 139, 147, 158, 168, 181, 193, 206, 220, 235, 256, 276, 297, 319, 346, 378, 409, 443, 476, 510, 545, 579, 613, more...

integer, monotonic, +, A076202 (weak, multiple)

a(n)=∑[∑[τ(n-τ(a(n-1)))]%n]
a(0)=1
τ(n)=number of divisors of n
∑(a)=partial sums of a
n≥2
9 operations
Prime

Sequence z4roqkjyje3pb

1, 1, 2, 4, 8, 13, 17, 21, 27, 34, 41, 47, 54, 64, 77, 86, 96, 110, 122, 133, 145, 157, 169, 182, 197, 210, 227, 241, 256, 278, 295, 312, 333, 352, 375, 396, 419, 438, 460, 483, 506, 529, 552, 578, 603, 628, 654, 680, 709, 734, more...

integer, monotonic, +, A076202 (weak, multiple)

a(n)=floor(n/2)+a(n-1)+Ω(a(n-1))
a(0)=1
Ω(n)=number of prime divisors of n
n≥0
9 operations
Prime