A153718 Numbers k such that the fractional part of (Pi-2)^k is less than 1/k.

1, 2, 23, 24, 35, 41, 65, 182, 72506, 107346

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

Comments

Numbers k such that fract((Pi-2)^k) < 1/k, where fract(x) = x-floor(x).

The next such number must be greater than 200000.

a(11) > 10^6. - Jon E. Schoenfield, Nov 15 2014

Examples

			a(3)=23 since fract((Pi-2)^23) = 0.0260069... < 1/23, but fract((Pi-2)^k) >= 1/k for 3 <= k <= 22.
		

Crossrefs

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

Programs

Mathematica

Select[Range[1000], N[FractionalPart[(Pi - 2)^#], 100] < (1/#) &] (* G. C. Greubel, Aug 25 2016 *)

PARI

lista(nn) = for (n=1, nn, default(realprecision, n); if (frac((Pi-2)^n) < 1/n, print1(n, ", "))); \\ Michel Marcus, Nov 16 2014