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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, 531441, 3645, 1485, 945, 4851, 1575, 13041, 2835, 18225, 295245, 4095, 3465, 50625, 2657205, 11025, 25515, 52650, 14175, 17955, 10395, 1476225, 215233605, 97020, 17325, 150094635296999121
(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 positive 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.
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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.
Sequence in context: A075200 A075198 A006405 this_sequence A026297 A109742 A072979
Adjacent sequences: A136105 A136106 A136107 this_sequence A136109 A136110 A136111
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KEYWORD
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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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EXTENSIONS
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6 new terms from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jan 21 2009
a(37) from Max Alekseyev (maxale(AT)gmail.com), May 13 2009
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