cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A322610 Numbers that are sums (of a nonempty sequence) of consecutive centered triangular numbers.

Original entry on oeis.org

1, 4, 5, 10, 14, 15, 19, 29, 31, 33, 34, 46, 50, 60, 64, 65, 77, 85, 96, 106, 109, 110, 111, 136, 141, 149, 160, 166, 170, 174, 175, 194, 195, 199, 226, 235, 245, 255, 258, 259, 260, 274, 302, 304, 316, 330, 335, 354, 361, 364, 365, 368, 369, 394, 409, 411, 434, 440, 460, 471, 490, 496, 500
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 20 2018

Keywords

Links

Crossrefs

Cf. A005448, A005918 (2 consec), A006003, A034706, A320728, A322468, A322611, A322638, A322640.

Programs

  • Mathematica
    anmax = 1000; nmax = Floor[Sqrt[2*anmax/3]] + 1; Select[Union[Flatten[Table[Sum[(3*k^2 + 3*k + 2)/2, {k, i, j}], {i, 0, nmax}, {j, i, nmax}]]], # <= anmax &] (* Vaclav Kotesovec, Dec 21 2018 *)

A322611 Numbers that are sums (of a nonempty sequence) of consecutive centered square numbers.

Original entry on oeis.org

1, 5, 6, 13, 18, 19, 25, 38, 41, 43, 44, 61, 66, 79, 84, 85, 102, 113, 127, 140, 145, 146, 181, 187, 198, 212, 221, 225, 230, 231, 258, 259, 265, 300, 313, 325, 326, 338, 343, 344, 365, 402, 404, 421, 439, 445, 470, 481, 483, 486, 488, 489, 524, 545, 547, 578, 585, 613, 626, 651, 660
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 20 2018

Keywords

Links

Crossrefs

Cf. A001844, A005900, A034705, A320728, A322479, A322610, A322638, A322640.

Programs

  • Mathematica
    anmax = 1000; nmax = Floor[Sqrt[anmax/2]] + 1; Select[Union[Flatten[Table[Sum[k^2 + (k + 1)^2, {k, i, j}], {i, 0, nmax}, {j, i, nmax}]]], # <= anmax &] (* Vaclav Kotesovec, Dec 21 2018 *)

A322638 Numbers that are sums of consecutive centered pentagonal numbers (A005891).

Original entry on oeis.org

0, 1, 6, 7, 16, 22, 23, 31, 47, 51, 53, 54, 76, 82, 98, 104, 105, 106, 127, 141, 158, 174, 180, 181, 182, 226, 233, 247, 264, 276, 280, 286, 287, 322, 323, 331, 374, 391, 405, 407, 421, 427, 428, 456, 502, 504, 526, 548, 555, 586, 601, 602, 607, 608, 609, 654, 681, 683, 722
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 21 2018

Keywords

Links

Crossrefs

Cf. A004068, A005891, A152043, A319184, A322610, A322611, A322640.

Programs

  • Maple
    L:= [seq((5*n^2+5*n+2)/2,n=0..30)]: N:= L[-1]:
S:=[0,op(ListTools:-PartialSums(L))]:
R:=select(`<=`,{0,seq(seq(S[n]-S[m],m=1..n-1),n=1..nops(S))},N):
sort(convert(R,list)); # Robert Israel, Mar 19 2023
  • Mathematica
    terms = 59;
nmax = 16; kmax = 9; (* empirical *)
T = Table[(5n^2 + 5n + 2)/2, {n, 0, nmax}];
Union[{0}, T, Table[k MovingAverage[T, k], {k, 2, kmax}] // Flatten][[1 ;; terms]] (* Jean-François Alcover, Dec 26 2018 *)

A320728 Numbers that are sums of consecutive odd squares (or centered octagonal numbers).

Original entry on oeis.org

0, 1, 9, 10, 25, 34, 35, 49, 74, 81, 83, 84, 121, 130, 155, 164, 165, 169, 202, 225, 251, 276, 285, 286, 289, 290, 361, 371, 394, 420, 441, 445, 454, 455, 514, 515, 529, 596, 625, 645, 650, 670, 679, 680, 683, 729, 802, 804, 841, 875, 885, 934, 959, 961, 968, 969, 970, 1044, 1089
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 21 2018

Keywords

Links

Crossrefs

Cf. A000447, A016754, A034705, A152043, A322610, A322611, A322637, A322638, A322640.

Programs

  • PARI
    ok(n)={my(i=sqrtint(n)); i=i-(i%2==0); while(i>0, my(a=i^2, j=i); while(j>0 && a<=n, if(a==n, return(1)); j-=2; a=a+j^2); i-=2); 0}
concat([0], select(ok, [1..1200])) \\ Antonio Roldán, Mar 12 2020

A322652 Numbers that are sums of consecutive heptagonal pyramidal numbers (A002413).

Original entry on oeis.org

0, 1, 8, 9, 26, 34, 35, 60, 86, 94, 95, 115, 175, 196, 201, 209, 210, 308, 311, 371, 397, 405, 406, 456, 504, 619, 645, 679, 705, 713, 714, 764, 880, 960, 1075, 1101, 1135, 1161, 1166, 1169, 1170, 1409, 1508, 1525, 1605, 1720, 1780, 1806, 1814, 1815, 1911, 1981, 2046, 2289, 2380
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 21 2018

Keywords

Links

Crossrefs

Cf. A002413, A002418, A321450, A322468, A322479, A322636, A322640, A322651, A322653.

Programs

  • Mathematica
    imax = 55;
A002413 = LinearRecurrence[{4, -6, 4, -1}, {1, 8, 26, 60}, imax];
Join[{0}, Table[A002413[[i ;; j]] // Total, {i, 1, imax}, {j, i, imax}] // Flatten // Union][[;; imax]] (* Jean-François Alcover, Nov 11 2024 *)
Showing 1-5 of 5 results.

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