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

1,1

Comments

The sequence contains every square greater than 1.

Conjecture: the sequence contains infinitely many primes.

Links

Table of n, a(n) for n=1..63.

Formula

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

Example

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

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 *)

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.

Sequence in context: A131827 A035245 A243191 * A310945 A310946 A265140

Adjacent sequences: A260644 A260645 A260646 * A260648 A260649 A260650

Keyword

nonn

Author

Arkadiusz Wesolowski, Dec 02 2015

Status

approved