A153710 - OEIS

%I #16 Mar 25 2019 17:20:05

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

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

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

%C The next such number must be greater than 100000.

%C a(17) > 300000. - _Robert Price_, Mar 25 2019

%e 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.

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

%o (PARI) isok(k) = frac(Pi^k) < 1/k; \\ _Michel Marcus_, Feb 11 2014

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

%Y Cf. A001672.

%K nonn,more

%O 1,2

%A _Hieronymus Fischer_, Jan 08 2009

%E a(16) from _Robert Price_, Mar 25 2019