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A322638
Numbers that are sums of consecutive centered pentagonal numbers (A005891).
6
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
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 *)
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 21 2018
STATUS
approved