A357529 Triangular numbers k such that 2*k cannot be expressed as a sum of two distinct triangular numbers.

0, 1, 6, 10, 15, 45, 55, 66, 91, 120, 136, 231, 276, 300, 406, 435, 496, 561, 595, 630, 741, 780, 820, 861, 1081, 1225, 1326, 1431, 1830, 2016, 2080, 2145, 2211, 2415, 2485, 2701, 2850, 3240, 3321, 3486, 3655, 3916, 4005, 4465, 4560, 4950, 5050, 5356, 5460, 5565

Offset

1,3

Comments

Subset of even terms of A357505, divided by 2. - Michel Marcus, Nov 05 2022

Links

Table of n, a(n) for n=1..50.

Mathematica

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 *)

Crossrefs

Cf. A000217 (supersequence), A002378.

Half of the complement of A357504 in A020756.

Half of the complement of A020757 in A357505.

Subsequence of A008851.

Sequence in context: A238047 A272398 A020159 * A048017 A332392 A048078

Adjacent sequences: A357526 A357527 A357528 * A357530 A357531 A357532

Keyword

nonn,easy

Author

Stefano Spezia, Oct 02 2022

Status

approved