A260647 Numbers that are the sum of two distinct nonzero triangular numbers.

4, 7, 9, 11, 13, 16, 18, 21, 22, 24, 25, 27, 29, 31, 34, 36, 37, 38, 39, 42, 43, 46, 48, 49, 51, 55, 56, 57, 58, 60, 61, 64, 65, 66, 67, 69, 70, 72, 73, 76, 79, 81, 83, 84, 87, 88, 91, 92, 93, 94, 97, 99, 100, 101, 102, 106, 108, 111, 112, 114, 115, 119, 120

Offset: 1

Author

Arkadiusz Wesolowski, Dec 02 2015

Keywords

• nonn

Comments

The sequence contains every square greater than 1.

Conjecture: the sequence contains infinitely many primes.

Examples

			24 = 3 + 21, so 24 is in the sequence.
		

Crossrefs

Cf. A000217, A265140 (exactly one way), A262749 (more than one way), A265134 (exactly two ways), A265135 (more than two ways), A265136 (exactly three ways), A265137 (more than three ways), A265138 (exactly four ways).

Subsequence of A051533.

Programs

Mathematica

r = 120; lst = Table[0, {r}]; lim = Floor[Sqrt[8*r - 7]]; Do[num = (i^2 + i)/2 + (j^2 + j)/2; If[num <= r, lst[[num]]++], {i, lim}, {j, i - 1}]; Flatten@Position[lst, n_ /; n > 0]
With[{nn=20},Select[Union[Total/@Subsets[Accumulate[Range[nn]],{2}]],#<= (nn(nn+1))/2+1&]] (* Harvey P. Dale, Jul 26 2020 *)

Formula

{k: A307597(k) > 0 }. - R. J. Mathar, Apr 28 2020