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 1-6 of 6 results.

A322468 Numbers that are sums of consecutive tetrahedral numbers.

Original entry on oeis.org

0, 1, 4, 5, 10, 14, 15, 20, 30, 34, 35, 55, 56, 65, 69, 70, 84, 91, 111, 120, 121, 125, 126, 140, 165, 175, 195, 204, 205, 209, 210, 220, 260, 285, 286, 295, 315, 325, 329, 330, 364, 369, 385, 425, 455, 460, 480, 490, 494, 495, 505, 506, 560, 589, 645, 650, 671, 680, 700
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 09 2018

Keywords

Examples

			209 = sum_{k=2..7} A000292(k) so 209 is in the list. 295=sum_{k=5..8} A000292(k), so 295 is in the list.

Links

Crossrefs

Cf. A000292 (tetrahedral numbers, a subsequence), A000330 (subsequence), A006003 (subsequence), A005894 (subsequence).
Other sums of consecutive numbers: A034705 (squares), A034706 (triangular numbers), A322479 (square pyramidal numbers), A322610 (centered triangular numbers), A322611 (centered square numbers).

Programs

  • Mathematica
    tet[n_] := n (n + 1) (n + 2)/6; nMax = 700; t = {0}; Do[k = n; s = 0; While[s = s + tet[k]; s <= nMax, AppendTo[t, s]; k++], {n, (6*nMax)^(1/3) + 1}]; t = Union[t] (* Amiram Eldar, Dec 09 2018 after T. D. Noe at A034705 *)
anmax = 1000; nmax = Floor[(6*anmax)^(1/3)] + 1; Select[Union[Flatten[Table[Sum[k*(k + 1)*(k + 2)/6, {k, i, j}], {i, 0, nmax}, {j, i, nmax}]]], # <= anmax &] (* Vaclav Kotesovec, Dec 21 2018 *)

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 *)

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

A322640 Numbers that are sums of consecutive centered heptagonal numbers (A069099).

Original entry on oeis.org

0, 1, 8, 9, 22, 30, 31, 43, 65, 71, 73, 74, 106, 114, 136, 144, 145, 148, 177, 197, 220, 242, 250, 251, 253, 254, 316, 325, 345, 368, 386, 390, 398, 399, 450, 451, 463, 522, 547, 565, 569, 587, 595, 596, 598, 638, 702, 704, 736, 766, 775, 818, 840, 841, 848, 849, 914, 953
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 21 2018

Keywords

Links

Crossrefs

Cf. A004126, A069099, A152043, A322610, A322611, A322636, A322638, A320728.

Programs

  • Mathematica
    terms = 58;
nmax = 17; kmax =  8; (* empirical *)
T = Table[(7 n^2 - 7 n + 2)/2, {n, 1, nmax}];
Union[{0}, T, Table[k MovingAverage[T, k], {k, 2, kmax}] // Flatten][[1 ;; terms]] (* Jean-François Alcover, Dec 27 2018 *)

A329636 Numbers that are sums of consecutive centered cube numbers (A005898).

Original entry on oeis.org

1, 9, 10, 35, 44, 45, 91, 126, 135, 136, 189, 280, 315, 324, 325, 341, 530, 559, 621, 656, 665, 666, 855, 900, 1089, 1180, 1215, 1224, 1225, 1241, 1414, 1729, 1755, 1944, 2035, 2070, 2079, 2080, 2096, 2331, 2655, 2970, 2996, 3059, 3185, 3276, 3311, 3320, 3321, 3825, 3925
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 18 2019

Keywords

Links

Crossrefs

Cf. A005898, A037270, A217843, A322611, A329634, A329635.
Showing 1-6 of 6 results.

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