A127025 Let f(n) = exp(Pi*sqrt(n)); sequence gives numbers n such that ceiling(f(n)) - f(n) < 1/10^6.

58, 163, 1467, 478233, 881967, 1053883, 1341615, 1844122, 3498092, 6069493, 6396611, 8707530, 10414308, 13340780, 16039620, 17013933, 17226343, 18577932, 19390220, 21991290, 24529596, 26202225, 26634713, 26651262, 26848308, 27497372, 32149837, 35437319, 35892748

Offset: 1

Author

Artur Jasinski, Jan 03 2007

Keywords

• nonn

Links

• Anthony Canu, Table of n, a(n) for n = 1..182

Crossrefs

Cf. A035484, A127022, A127023, A127024.

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^(-6)), AppendTo[a, x]], {x, 1, 1000}]; a

PARI

is(n)=my(t);default(realprecision, 40);default(realprecision, Pi*sqrt(n)\log(10)+40); t=exp(Pi*sqrt(n));ceil(t)-t<1e-6 \\ Charles R Greathouse IV, Feb 20 2012

Extensions

a(4)-a(20) from Charles R Greathouse IV, Feb 20 2012

a(21)-a(36) from Charles R Greathouse IV, Feb 23 2012