A127022 Let f(k) = exp(Pi*sqrt(k)); sequence gives numbers k such that ceiling(f(k)) - f(k) < 1/10^3.

25, 37, 43, 58, 67, 74, 163, 232, 522, 719, 1169, 1245, 1467, 1850, 1872, 2086, 3368, 4075, 5773, 7685, 7802, 7942, 8325, 9728, 10032, 11682, 12158, 13574, 17908, 18505, 19183, 19396, 20039, 20244, 20584, 22241, 23773, 23778, 23834, 25004, 27573, 28071, 32497

Offset: 1

Author

Artur Jasinski, Jan 03 2007

Keywords

• nonn

Links

• JungHwan Min, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A035484, A127023, A127024, A127025.

Programs

Magma

SetDefaultRealField(RealField(500)); R:= RealField(); [n: n in [1..50000] | Ceiling(Exp(Pi(R)*Sqrt(n))) - Exp(Pi(R)*Sqrt(n)) lt 1/1000]; // G. C. Greubel, Jun 02 2019

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^(-3)), AppendTo[a, x]], {x, 1, 1000}]; a
Reap[Block[{$MaxExtraPrecision = Infinity}, Do[If[N[FractionalPart[Exp[Pi Sqrt[n]]], 8] > .999, Sow[n]], {n, 2000}]]][[-1, 1]] (* JungHwan Min, Mar 20 2016 *)

PARI

default(realprecision, 500); c(n) = exp(Pi*sqrt(n));
for(n=1, 50000, if( ceil(c(n)) - c(n) <1/1000, print1(n", "))) \\ G. C. Greubel, Jun 02 2019

Extensions

a(16)-a(43) added (from JungHwan Min's b-file) by Jon E. Schoenfield, Sep 04 2017