A357504 -id:A357504 - cp's OEIS frontend

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

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 *)

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

Original entry on oeis.org

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

Stefano Spezia, Oct 02 2022

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

Cf. A000217 (supersequence), A002378.
Half of the complement of A357504 in A020756.
Half of the complement of A020757 in A357505.
Subsequence of A008851.

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 *)

cp's OEIS Frontend

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

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