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A260647
Numbers that are the sum of two distinct nonzero triangular numbers.
10
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved