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

%I A322638 #16 Feb 16 2025 08:33:57
%S A322638 0,1,6,7,16,22,23,31,47,51,53,54,76,82,98,104,105,106,127,141,158,174,
%T A322638 180,181,182,226,233,247,264,276,280,286,287,322,323,331,374,391,405,
%U A322638 407,421,427,428,456,502,504,526,548,555,586,601,602,607,608,609,654,681,683,722
%N A322638 Numbers that are sums of consecutive centered pentagonal numbers (A005891).
%H A322638 Robert Israel, <a href="/A322638/b322638.txt">Table of n, a(n) for n = 1..10000</a>
%H A322638 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredPentagonalNumber.html">Centered Pentagonal Number</a>
%p A322638 L:= [seq((5*n^2+5*n+2)/2,n=0..30)]: N:= L[-1]:
%p A322638 S:=[0,op(ListTools:-PartialSums(L))]:
%p A322638 R:=select(`<=`,{0,seq(seq(S[n]-S[m],m=1..n-1),n=1..nops(S))},N):
%p A322638 sort(convert(R,list)); # _Robert Israel_, Mar 19 2023
%t A322638 terms = 59;
%t A322638 nmax = 16; kmax = 9; (* empirical *)
%t A322638 T = Table[(5n^2 + 5n + 2)/2, {n, 0, nmax}];
%t A322638 Union[{0}, T, Table[k MovingAverage[T, k], {k, 2, kmax}] // Flatten][[1 ;; terms]] (* _Jean-François Alcover_, Dec 26 2018 *)
%Y A322638 Cf. A004068, A005891, A152043, A319184, A322610, A322611, A322640.
%K A322638 nonn
%O A322638 1,3
%A A322638 _Ilya Gutkovskiy_, Dec 21 2018