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Search: id:A045899
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| A045899 |
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Numbers n such that n+1 and 3*n+1 are perfect squares. |
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+0
5
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| 0, 8, 120, 1680, 23408, 326040, 4541160, 63250208, 880961760, 12270214440, 170902040408, 2380358351280, 33154114877520, 461777249934008, 6431727384198600
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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A. Baker and H. Davenport, The equations 3x^2-2=y^2 and 8x^2-7=z^2, Quart. J. Math. Oxford Ser. (2) 20 (1969), 129-137.
A. Dujella and A. Pethoe, A generalization of a theorem of Baker and Davenport, Quart. J. Math. Oxford Ser. (2) 49 (1998), 291-306.
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LINKS
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A. Dujella, The Problem of Diophantus and Davenport, References
A. Dujella, Publications of Andrej Dujella
P. Gibbs, 1,3,8,120 ... A Diophantine Problem
P. Gibbs, Diophantine quadruples and Cayley's hyperdeterminant.
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FORMULA
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a(k)=14*a(k-1)-a(k-2)+8
a[k] = ((Sqrt[3]+2)*(7+4*Sqrt[3])^k - (Sqrt[3]-2)(7-4*Sqrt[3])^k - 4)/6 - Joseph Biberstine (jrbibers(AT)indiana.edu), Apr 23 2006
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MATHEMATICA
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FullSimplify[Table[((Sqrt[3]+2)*(7+4*Sqrt[3])^k - (Sqrt[3]-2)(7-4*Sqrt[3])^k - 4)/6, {k, 0, 40}]] - Joseph Biberstine (jrbibers(AT)indiana.edu), Apr 23 2006
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CROSSREFS
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Equals A046184(n+1) - 1.
Essentially the same as A051047. Cf. A067900.
Sequence in context: A116008 A086302 A053129 this_sequence A004381 A130979 A133308
Adjacent sequences: A045896 A045897 A045898 this_sequence A045900 A045901 A045902
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KEYWORD
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nonn
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AUTHOR
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Andrej Dujella (duje(AT)math.hr)
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