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A322636 Numbers that are sums of consecutive heptagonal numbers (A000566).

%I A322636 #15 May 22 2025 16:43:35
%S A322636 0,1,7,8,18,25,26,34,52,55,59,60,81,89,107,112,114,115,136,148,170,
%T A322636 188,189,193,195,196,235,248,260,282,286,300,307,308,337,341,342,396,
%U A322636 403,424,430,448,449,455,456,469,521,530,540,572,585,616,619,628,637,644,645,684,697
%N A322636 Numbers that are sums of consecutive heptagonal numbers (A000566).
%H A322636 Robert Israel, <a href="/A322636/b322636.txt">Table of n, a(n) for n = 1..10000</a>
%H A322636 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeptagonalNumber.html">Heptagonal Number</a>
%p A322636 N:= 1000: # for terms up to N
%p A322636 Hepta:= [seq(n*(5*n-3)/2,n=0..floor((3+sqrt(9+40*N))/10))]:
%p A322636 PS:= ListTools:-PartialSums(Hepta):
%p A322636 S:= select(`<=`,{0,seq(seq(PS[i]-PS[j],j=1..i-1),i=1..nops(PS))},N):
%p A322636 sort(convert(S,list)); # _Robert Israel_, May 22 2025
%t A322636 terms = 59;
%t A322636 nmax = 17; kmax = 9; (* empirical *)
%t A322636 T = Table[n(5n-3)/2, {n, 0, nmax}];
%t A322636 Union[T, Table[k MovingAverage[T, k], {k, 2, kmax}]//Flatten][[1 ;; terms]] (* _Jean-François Alcover_, Dec 26 2018 *)
%Y A322636 Cf. A000566, A002413, A034705, A034706, A319184, A319185, A322637.
%K A322636 nonn
%O A322636 1,3
%A A322636 _Ilya Gutkovskiy_, Dec 21 2018