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A322637 Numbers that are sums of consecutive octagonal numbers (A000567).

%I A322637 #14 May 22 2025 16:37:37
%S A322637 0,1,8,9,21,29,30,40,61,65,69,70,96,105,126,133,134,135,161,176,201,
%T A322637 222,225,229,230,231,280,294,309,334,341,355,363,364,401,405,408,470,
%U A322637 481,505,510,531,534,539,540,560,621,630,645,681,695,735,736,749,756,764,765,814,833,846
%N A322637 Numbers that are sums of consecutive octagonal numbers (A000567).
%H A322637 Robert Israel, <a href="/A322637/b322637.txt">Table of n, a(n) for n = 1..10000</a>
%H A322637 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number</a>
%p A322637 N:= 1000: # for terms up to N
%p A322637 Octa:= [seq(n*(3*n-2),n=0..floor((1+sqrt(1+3*N))/3))]:
%p A322637 PS:= ListTools:-PartialSums(Octa):
%p A322637 S:= select(`<=`,{0,seq(seq(PS[i]-PS[j],j=1..i-1),i=1..nops(PS))},N):
%p A322637 sort(convert(S,list)); # _Robert Israel_, May 22 2025
%t A322637 terms = 60;
%t A322637 nmax = 17; kmax = 9; (* empirical *)
%t A322637 T = Table[n(3n-2), {n, 0, nmax}];
%t A322637 Union[T, Table[k MovingAverage[T, k], {k, 2, kmax}]//Flatten][[1 ;; terms]] (* _Jean-François Alcover_, Dec 26 2018 *)
%Y A322637 Cf. A000567, A002414, A034705, A034706, A319184, A319185, A322636.
%K A322637 nonn
%O A322637 1,3
%A A322637 _Ilya Gutkovskiy_, Dec 21 2018