A035484 Numbers n such that fractional part of e^(Pi*sqrt(n)) > 0.99.

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

Offset: 1

Author

Erich Friedman

Keywords

• nonn

Comments

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

Examples

			e^(Pi*sqrt(163)) = 262537412640768743.9999999999992
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A019296, A127022, A127023, A127024, A127025.

Programs

Mathematica

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 *)

Extensions

Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar