The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #10 May 29 2016 17:13:48
%S 1,4,5,7,10,13,16,19,21,22,25,28,40,42,59,60,64,76,85,89,93,109,110,
%T 124,127,142,144,148,161,165,178,184,195,212,229,233,246,247,263,265,
%U 268,280,297,313,314,331,346,348,349,365,373,376,382,399,416,433,445,450
%N Numbers k such that triangular(k) - m is a triangular number (A000217), where m is the largest square less than triangular(k).
%C The sequence of triangular(a(n)) begins: 1, 10, 15, 28, 55, 91, 136, 190, 231, 253, 325, ...
%H Ivan Neretin, <a href="/A234141/b234141.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range[450], IntegerQ@Sqrt[8 ((#^2 + #)/2 - (Ceiling@Sqrt[(#^2 + #)/2] - 1)^2) + 1] &] (* _Ivan Neretin_, May 29 2016 *)
%Y Cf. A000217, A000290, A234142, A234143.
%K nonn
%O 1,2
%A _Alex Ratushnyak_, Dec 19 2013