A357529 -id:A357529 - cp's OEIS frontend

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

Offset: 1

Stefano Spezia, Oct 01 2022

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.

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

Cf. A357529.

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]A000217[h]] && k>kn, AppendTo[a, k]; kn=k]]]; a (* Stefano Spezia, Nov 06 2022 *)

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

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

Original entry on oeis.org

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

Stefano Spezia, Oct 01 2022

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.

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

Cf. A357529.

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]A000217[h]] , ok=0]]; If[ok==1, AppendTo[a, k]]]; a (* Stefano Spezia, Nov 06 2022 *)

cp's OEIS Frontend

A357504 Numbers that are the sum of two distinct triangular numbers.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula