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Search: id:A101903
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| A101903 |
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Number of twin Pythagorean triples with hypotenuse less than 10^n. |
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+0
1
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| 1, 7, 24, 74, 228, 712, 2243, 7079, 22370, 70722, 223619, 707120, 2236083, 7071084, 22360697, 70710696, 223606818, 707106802, 2236067999, 7071067836, 22360679800, 70710678145, 223606797778, 707106781216, 2236067977530
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) <= 10^(n/2)/Sqrt(2). - Robert G. Wilson v Jan 08 2005.
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LINKS
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Eric Weisstein's World of Mathematics, Twin Pythagorean Triple
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EXAMPLE
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For a(2)=7 because {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {20, 21, 29}, {9, 40, 41}, {11, 60, 61}, {13, 84, 85}.
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MATHEMATICA
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f[n_] := Round[ Sqrt[ (10^n - 1)/2] - 1]; a[n_] := (MatrixPower[{{1, 2, 2}, {2, 1, 2}, {2, 2, 3}}, n].{{1}, {0}, {1}})[[3, 1]]; t = Table[ a[n], {n, 2, 35}]; g[n_] := Length[ Select[t, # < 10^n &]]; Table[f[n] + g[n], {n, 25}] (from Robert G. Wilson v Jan 08 2005)
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CROSSREFS
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Sequence in context: A014205 A029585 A114291 this_sequence A050191 A021000 A129797
Adjacent sequences: A101900 A101901 A101902 this_sequence A101904 A101905 A101906
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Dec 20, 2004
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EXTENSIONS
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a(5) and up from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 08 2005
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