A127020 Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that ceiling(f(n))-f(n) < 1/10.

6, 7, 13, 17, 18, 22, 25, 27, 28, 31, 37, 43, 58, 59, 67, 74, 84, 88, 94, 125, 127, 129, 136, 149, 162, 163, 174, 177, 183, 213, 217, 232, 240, 247, 267, 273, 279, 282, 295, 301, 304, 307, 321, 322, 326, 333, 337, 352, 355, 357, 365, 385, 386, 388, 389, 396, 439

Offset: 1

Author

Artur Jasinski, Jan 03 2007

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A035484, A127022, A127023, A127024, A127025.

Programs

Magma

SetDefaultRealField(RealField(500)); R:= RealField(); [n: n in [1..500] | Ceiling(Exp(Pi(R)*Sqrt(n))) - Exp(Pi(R)*Sqrt(n)) lt 1/10]; // G. C. Greubel, May 31 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^(-1)), AppendTo[a, x]], {x, 1, 1000}]; a
epQ[n_]:=Module[{c=Exp[Pi Sqrt[n]]},Ceiling[c]-c<1/10]; Select[ Range[ 500], epQ] (* Harvey P. Dale, May 10 2015 *)

PARI

default(realprecision, 500); c(n) = exp(Pi*sqrt(n));
for(n=1, 500, if( ceil(c(n)) - c(n) <1/10, print1(n", "))) \\ G. C. Greubel, May 31 2019