A319184 Numbers that are sums of consecutive pentagonal numbers.

0, 1, 5, 6, 12, 17, 18, 22, 34, 35, 39, 40, 51, 57, 69, 70, 74, 75, 86, 92, 108, 117, 120, 121, 125, 126, 145, 156, 162, 176, 178, 190, 195, 196, 209, 210, 213, 247, 248, 262, 270, 279, 282, 287, 288, 321, 330, 354, 365, 376, 386, 387, 399, 404, 405, 424, 425, 438, 457, 475

Offset

1,3

Links

Table of n, a(n) for n=1..60.

Eric Weisstein's World of Mathematics, Pentagonal Number

Mathematica

anmax = 1000; nmax = Floor[Sqrt[2*anmax/3]] + 1; Select[Union[Flatten[Table[Sum[k*(3*k-1)/2, {k, i, j}], {i, 0, nmax}, {j, i, nmax}]]], # <= anmax &] (* Vaclav Kotesovec, Dec 21 2018 *)
Module[{nn=20, pn}, pn=PolygonalNumber[5, Range[0, nn]]; Take[Union[Flatten[Table[Total/@Partition[pn, d, 1], {d, nn}]]], 60]] (* Harvey P. Dale, Jun 22 2025 *)

Crossrefs

Cf. A000326, A002411, A034705, A034706, A319185, A322636, A322637.

Sequence in context: A032707 A240756 A127306 * A231959 A362948 A168145

Adjacent sequences: A319181 A319182 A319183 * A319185 A319186 A319187

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 21 2018

Status

approved