A357505 Numbers that are not sum of two distinct triangular numbers.

0, 2, 5, 8, 12, 14, 17, 19, 20, 23, 26, 30, 32, 33, 35, 40, 41, 44, 47, 50, 52, 53, 54, 59, 62, 63, 68, 71, 74, 75, 77, 80, 82, 85, 86, 89, 90, 95, 96, 98, 103, 104, 107, 109, 110, 113, 116, 117, 118, 122, 124, 125, 128, 129, 131, 132, 134, 138, 140, 143, 145, 147

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..62.

Mathematica

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 *)

Crossrefs

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

Cf. A357529.

Sequence in context: A004112 A024815 A073837 * A189531 A190347 A193767

Adjacent sequences: A357502 A357503 A357504 * A357506 A357507 A357508

Keyword

nonn,easy

Author

Stefano Spezia, Oct 01 2022

Status

approved