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A051533
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Numbers which are the sum of two positive triangular numbers.
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15
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2, 4, 6, 7, 9, 11, 12, 13, 16, 18, 20, 21, 22, 24, 25, 27, 29, 30, 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, 90, 91, 92, 93, 94, 97, 99, 100, 101, 102, 106, 108
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Source
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EXAMPLE
| 666 is in the sequence because we can write 666 = 435 + 231 = binomial(22,2)+binomial(30,2).
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MATHEMATICA
| f[k_] := If[!
Head[Reduce[m (m + 1) + n (n + 1) == 2 k && 0 < m && 0 < n, {m, n},
Integers]] === Symbol, k, 0]; DeleteCases[Table[f[k], {k, 1, 108}], 0] (added by Ant King 22 Nov 2010)
nn=50; tri=Table[n(n+1)/2, {n, nn}]; Select[Union[Flatten[Table[tri[[i]]+tri[[j]], {i, nn}, {j, i, nn}]]], #<=tri[[-1]] &]
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CROSSREFS
| Cf. A000217, A020756 (sums of two triangular numbers), A001481 (sums of two squares), A007294, A051611.
Sequence in context: A052056 A187974 A193715 * A186151 A184732 A039009
Adjacent sequences: A051530 A051531 A051532 * A051534 A051535 A051536
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)
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