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Search: id:A136108
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| A136108 |
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The least number, k, such that there are n different representations of k as the difference of two positive triangular numbers. |
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+0
2
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| 1, 2, 5, 9, 27, 45, 63, 105, 135, 225, 405, 630, 315
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The first occurrence of n in A136107
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EXAMPLE
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a(0)=1 because there are no two triangular numbers whose
difference is 1,
a(1)=2 because 3-1 = 2,
a(2)=5 because 6-1 = 15-10 = 5,
a(3)=9 because 10-1 = 15-6 = 45-36 = 9, etc.
Also a(14) = 3645, a(15) = 1485, a(16) = 945, a(17) = 4851, a(18) = 1575, a(19) = 13041, a(20) = 2835, a(21) = 18225, a(23) = 4095, a(24) = 3465,
a(25) = 50625, a(27) = 11025, a(28) = 25515, a(29) = 52650, a(30) = 14175, a(31) = 17955, a(32) = 10395, a(36) = 17325, a(40) = 31185, a(48) = 45045, ...
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MATHEMATICA
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f[n_] := f[n] = Block[{c = 0, k = 1}, While[k < n, If[IntegerQ[Sqrt[8 n + 4 k (k + 1) + 1]], c++ ]; k++ ]; c]; Table[ Position[ Table[ f@i, {i, 54000}], n, 1, 1], {n, 0, 30}] // Flatten
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CROSSREFS
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Cf. A136107.
Adjacent sequences: A136105 A136106 A136107 this_sequence A136109 A136110 A136111
Sequence in context: A075200 A075198 A006405 this_sequence A026297 A109742 A072979
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KEYWORD
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more,nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu) and Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 12 2007
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