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A035484
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Numbers n such that fractional part of e^(Pi*sqrt(n)) > 0.99.
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15
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6, 17, 18, 22, 25, 37, 43, 58, 59, 67, 74, 149, 163, 177, 232, 267, 326, 386, 522, 566, 638, 719, 790, 792, 928, 986, 1014, 1169, 1245, 1257, 1293, 1326, 1467, 1556, 1850, 1872, 1960, 2061, 2086, 2160, 2196, 2208, 2278, 2403, 2438, 2551, 2653, 2795, 2829
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OFFSET
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1,1
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COMMENTS
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Equivalently, let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that ceiling(f(n)) - f(n) < 1/10^2. - Artur Jasinski, Jan 03 2007
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LINKS
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EXAMPLE
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e^(Pi*sqrt(163)) = 262537412640768743.9999999999992
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MATHEMATICA
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a = {}; Do[If[(1 - (Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]]) > 0) && (1 - ( Exp[Pi Sqrt[x]] - Floor[Exp[Pi Sqrt[x]]])< 10^(-2)), AppendTo[a, x]], {x, 1, 1000}]; a (* Artur Jasinski, Jan 03 2007 *)
Block[{$MaxExtraPrecision = 1000}, Select[Range@ 3000, And[1 - (#1 - #2) > 0, 1 - (#1 - #2) < 10^(-2)] & @@ {#, Floor@ #} &@ Exp[Pi*Sqrt[#]] &]] (* Michael De Vlieger, Sep 04 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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