A153723 Greatest number m such that the fractional part of (Pi-2)^A153719(m) >= 1-(1/m).

1, 1, 1, 3, 16, 24, 45, 158, 410, 946, 1182, 8786, 16159, 20188, 61392, 78800, 78959, 217556

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

Examples

			a(5) = 16, since 1-(1/17) = 0.941176... > fract((Pi-2)^A153719(5)) = fract((Pi-2)^5) = 0.9389... >= 0.9375 = 1-(1/16).
		

Crossrefs

Cf. A153663, A153671, A153679, A153687, A153695, A091560, A153711, A153719, A154130.

Programs

Mathematica

$MaxExtraPrecision = 100000;
A153719 = {1, 2, 3, 4, 5, 39, 56, 85, 557, 911, 2919, 2921, 4491,
   11543, 15724, 98040, 110932, 126659};
Floor[1/(1 - FractionalPart[(Pi - 2)^A153719])] (* Robert Price, Apr 18 2019 *)

Formula

a(n) = floor(1/(1-fract((Pi-2)^A153719(n)))), where fract(x) = x-floor(x).