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

0, 1, 8, 9, 21, 29, 30, 40, 61, 65, 69, 70, 96, 105, 126, 133, 134, 135, 161, 176, 201, 222, 225, 229, 230, 231, 280, 294, 309, 334, 341, 355, 363, 364, 401, 405, 408, 470, 481, 505, 510, 531, 534, 539, 540, 560, 621, 630, 645, 681, 695, 735, 736, 749, 756, 764, 765, 814, 833, 846

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, Octagonal Number

Crossrefs

Cf. A000567, A002414, A034705, A034706, A319184, A319185, A322636.

Programs

Maple

N:= 1000: # for terms up to N
Octa:= [seq(n*(3*n-2),n=0..floor((1+sqrt(1+3*N))/3))]:
PS:= ListTools:-PartialSums(Octa):
S:= select(`<=`,{0,seq(seq(PS[i]-PS[j],j=1..i-1),i=1..nops(PS))},N):
sort(convert(S,list)); # Robert Israel, May 22 2025

Mathematica

terms = 60;
nmax = 17; kmax = 9; (* empirical *)
T = Table[n(3n-2), {n, 0, nmax}];
Union[T, Table[k MovingAverage[T, k], {k, 2, kmax}]//Flatten][[1 ;; terms]] (* Jean-François Alcover, Dec 26 2018 *)