A153714 Greatest number m such that the fractional part of Pi^A153710(n) <= 1/m.

7, 159, 50, 10, 21, 55, 117, 270, 307, 744, 757, 7804, 13876, 62099, 70718, 154755

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

Examples

			a(2)=159 since 1/160<fract(Pi^A153710(2))=fract(Pi^3)=0.0062766...<=1/159.
		

Crossrefs

Cf. A153662, A153670, A153678, A153686, A153694, A153702, A153710, A154130, A153722.

Cf. A001672.

Programs

Mathematica

A153710 = {1, 3, 5, 9, 10, 11, 59, 81, 264, 281, 472, 3592, 10479,
   12128, 65875, 118885};
Table[fp = FractionalPart[Pi^A153710[[n]]]; m = Floor[1/fp];
While[fp <= 1/m, m++]; m - 1, {n, 1, Length[A153710]}] (* Robert Price, May 10 2019 *)

Formula

a(n) = floor(1/fract(Pi^A153710(n))), where fract(x) = x-floor(x).

Extensions

a(16) from Robert Price, May 10 2019