A153710 Numbers k such that the fractional part of Pi^k is less than 1/k.

1, 3, 5, 9, 10, 11, 59, 81, 264, 281, 472, 3592, 10479, 12128, 65875, 118885

Offset: 1

Author

Hieronymus Fischer, Jan 08 2009

Keywords

• nonn
• more

Comments

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

The next such number must be greater than 100000.

a(17) > 300000. - Robert Price, Mar 25 2019

Examples

			a(4) = 9 since fract(Pi^9) = 0.0993... < 1/9, but fract(Pi^k) = 0.3891..., 0.2932..., 0.5310... for 6 <= k <= 8, which all are greater than 1/k.
		

Crossrefs

Cf. A153662, A153670, A153678, A153686, A153694, A153702, A153714, A154130, A153718.

Cf. A001672.

Programs

Mathematica

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

PARI

isok(k) = frac(Pi^k) < 1/k; \\ Michel Marcus, Feb 11 2014

Extensions

a(16) from Robert Price, Mar 25 2019