%I #16 Jun 04 2023 08:56:08

%S 0,2,5,8,12,14,17,19,20,23,26,30,32,33,35,40,41,44,47,50,52,53,54,59,

%T 62,63,68,71,74,75,77,80,82,85,86,89,90,95,96,98,103,104,107,109,110,

%U 113,116,117,118,122,124,125,128,129,131,132,134,138,140,143,145,147

%N Numbers that are not sum of two distinct triangular numbers.

%C This sequence differs from A020757 in including the terms that are twice a triangular number and that cannot be expressed as a sum of two distinct triangular numbers: 0, 2, 12, 20, 30, 90, 110, 132, ... = 2*A357529.

%t TriangularQ[n_]:=IntegerQ[(Sqrt[1+8n]-1)/2]; A000217[n_]:=n(n+1)/2; a={}; For[k=0, k<=148, k++, ok=1; For[h=0, A000217[h]<k/2, h++, If[TriangularQ[k - A000217[h]] , ok=0]]; If[ok==1, AppendTo[a, k]]]; a (* _Stefano Spezia_, Nov 06 2022 *)

%Y Cf. A000217, A020757 (subsequence), A357504 (complement).

%Y Cf. A357529.

%K nonn,easy

%O 1,2

%A _Stefano Spezia_, Oct 01 2022