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%I #19 Nov 06 2022 14:51:44
%S 0,1,6,10,15,45,55,66,91,120,136,231,276,300,406,435,496,561,595,630,
%T 741,780,820,861,1081,1225,1326,1431,1830,2016,2080,2145,2211,2415,
%U 2485,2701,2850,3240,3321,3486,3655,3916,4005,4465,4560,4950,5050,5356,5460,5565
%N Triangular numbers k such that 2*k cannot be expressed as a sum of two distinct triangular numbers.
%C Subset of even terms of A357505, divided by 2. - _Michel Marcus_, Nov 05 2022
%t TriangularQ[n_]:=IntegerQ[(Sqrt[1+8n]-1)/2]; A000217[n_]:=n(n+1)/2; a={}; For[k=0, k<=105, k++, ok=1; For[h=0, h<2k, h++, If[TriangularQ[2*A000217[k] - A000217[h]] && k!=h, ok=0]]; If[ok==1, AppendTo[a,k(k+1)/2]]]; a (* _Stefano Spezia_, Nov 05 2022 *)
%Y Cf. A000217 (supersequence), A002378.
%Y Half of the complement of A357504 in A020756.
%Y Half of the complement of A020757 in A357505.
%Y Subsequence of A008851.
%K nonn,easy
%O 1,3
%A _Stefano Spezia_, Oct 02 2022