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%I #15 Feb 16 2025 08:33:57
%S 1,4,5,10,14,15,19,29,31,33,34,46,50,60,64,65,77,85,96,106,109,110,
%T 111,136,141,149,160,166,170,174,175,194,195,199,226,235,245,255,258,
%U 259,260,274,302,304,316,330,335,354,361,364,365,368,369,394,409,411,434,440,460,471,490,496,500
%N Numbers that are sums (of a nonempty sequence) of consecutive centered triangular numbers.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredTriangularNumber.html">Centered Triangular Number</a>
%t anmax = 1000; nmax = Floor[Sqrt[2*anmax/3]] + 1; Select[Union[Flatten[Table[Sum[(3*k^2 + 3*k + 2)/2, {k, i, j}], {i, 0, nmax}, {j, i, nmax}]]], # <= anmax &] (* _Vaclav Kotesovec_, Dec 21 2018 *)
%Y Cf. A005448, A005918 (2 consec), A006003, A034706, A320728, A322468, A322611, A322638, A322640.
%K nonn,changed
%O 1,2
%A _Ilya Gutkovskiy_, Dec 20 2018