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 1-7 of 7 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 *)

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 *)

A321450 Numbers that are sums of consecutive pentagonal pyramidal numbers (A002411).

Original entry on oeis.org

0, 1, 6, 7, 18, 24, 25, 40, 58, 64, 65, 75, 115, 126, 133, 139, 140, 196, 201, 241, 259, 265, 266, 288, 322, 397, 405, 437, 455, 461, 462, 484, 550, 610, 685, 693, 725, 726, 743, 749, 750, 889, 936, 955, 1015, 1090, 1130, 1148, 1154, 1155, 1183, 1243, 1276, 1439
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 21 2018

Keywords

Links

Crossrefs

Cf. A001296, A002411, A319184, A322468, A322479, A322638, A322651, A322652, A322653.

A322651 Numbers that are sums of consecutive hexagonal pyramidal numbers (A002412).

Original entry on oeis.org

0, 1, 7, 8, 22, 29, 30, 50, 72, 79, 80, 95, 145, 161, 167, 174, 175, 252, 256, 306, 328, 335, 336, 372, 413, 508, 525, 558, 580, 587, 588, 624, 715, 785, 880, 897, 930, 946, 952, 959, 960, 1149, 1222, 1240, 1310, 1405, 1455, 1477, 1484, 1485, 1547, 1612, 1661, 1864, 1925
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 21 2018

Keywords

Links

Crossrefs

Cf. A002412, A002417, A152043, A319185, A321450, A322468, A322479, A322652, A322653.

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 *)

A322653 Numbers that are sums of consecutive octagonal pyramidal numbers (A002414).

Original entry on oeis.org

0, 1, 9, 10, 30, 39, 40, 70, 100, 109, 110, 135, 205, 231, 235, 244, 245, 364, 366, 436, 466, 475, 476, 540, 595, 730, 765, 800, 830, 839, 840, 904, 1045, 1135, 1270, 1305, 1340, 1370, 1379, 1380, 1386, 1669, 1794, 1810, 1900, 2035, 2105, 2135, 2144, 2145, 2275, 2350, 2431, 2714
Offset: 1

Views

Author

Ilya Gutkovskiy, Dec 21 2018

Keywords

Links

Crossrefs

Cf. A002414, A002419, A320728, A321450, A322468, A322479, A322637, A322651, A322652.

A329072 Numbers that are sums of consecutive octahedral numbers (A005900).

Original entry on oeis.org

0, 1, 6, 7, 19, 25, 26, 44, 63, 69, 70, 85, 129, 146, 148, 154, 155, 231, 275, 294, 300, 301, 344, 377, 462, 489, 506, 525, 531, 532, 575, 670, 721, 806, 833, 850, 869, 875, 876, 891, 1064, 1156, 1159, 1210, 1295, 1339, 1358, 1364, 1365, 1469, 1503, 1561, 1734
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 18 2019

Keywords

Links

Crossrefs

Cf. A005900, A006325, A217843, A322468, A322479, A329597, A329599.
Showing 1-7 of 7 results.

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