A357504 - OEIS

A357504

Numbers that are the sum of two distinct triangular numbers.

1, 3, 4, 6, 7, 9, 10, 11, 13, 15, 16, 18, 21, 22, 24, 25, 27, 28, 29, 31, 34, 36, 37, 38, 39, 42, 43, 45, 46, 48, 49, 51, 55, 56, 57, 58, 60, 61, 64, 65, 66, 67, 69, 70, 72, 73, 76, 78, 79, 81, 83, 84, 87, 88, 91, 92, 93, 94, 97, 99, 100, 101, 102, 105, 106, 108

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OFFSET

1,2

COMMENTS

This sequence differs from A020756 in excluding 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..66.

FORMULA

a(n) = (A339952(n) - 1)/4.

MATHEMATICA

TriangularQ[n_]:=IntegerQ[(Sqrt[1+8n]-1)/2]; A000217[n_]:=n(n+1)/2; a={}; kn=0; For[k=0, k<=110, k++, For[h=0, A000217[h]<k/2, h++, If[TriangularQ[k - A000217[h]] && k>kn, AppendTo[a, k]; kn=k]]]; a (* Stefano Spezia, Nov 06 2022 *)

CROSSREFS

Cf. A000217 (subsequence, excluding 0), A020756 (supersequence), A339952, A357505 (complement).

Cf. A357529.

Sequence in context: A298109 A184429 A248185 * A130269 A290730 A369856

Adjacent sequences: A357501 A357502 A357503 * A357505 A357506 A357507

KEYWORD

nonn,easy

AUTHOR

Stefano Spezia, Oct 01 2022

STATUS

approved