A153712 Numbers k such that the fractional part of Pi^k is greater than 1-(1/k).

1, 2, 15, 22, 58, 109, 157, 1030, 1071, 1274, 2008, 2322, 5269, 151710

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

Comments

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

The next such number must be greater than 100000.

a(15) > 300000. - Robert Price, Mar 25 2019

Examples

			a(3) = 15, since fract(Pi^15) = 0.969... > 0.933... = 1 - (1/15), but fract(Pi^k) <= 1 - (1/k) for 3 <= k <= 14.
		

Crossrefs

Cf. A153664, A153672, A153680, A153688, A153696, A153704, A153716, A154130, A153720.

Cf. A001672.

Programs

Mathematica

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

Extensions

a(14) from Robert Price, Mar 25 2019