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

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

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Centered Pentagonal Number

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 *)

Crossrefs

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

Sequence in context: A315844 A308903 A315845 * A309481 A308867 A315846

Adjacent sequences: A322635 A322636 A322637 * A322639 A322640 A322641

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 21 2018

Status

approved