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

Author

Ilya Gutkovskiy, Dec 21 2018

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Centered Pentagonal Number

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 *)