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%I #16 Mar 25 2019 17:19:59
%S 1,2,15,22,58,109,157,1030,1071,1274,2008,2322,5269,151710
%N Numbers k such that the fractional part of Pi^k is greater than 1-(1/k).
%C Numbers k such that fract(Pi^k) > 1-(1/k), where fract(x) = x-floor(x).
%C The next such number must be greater than 100000.
%C a(15) > 300000. - _Robert Price_, Mar 25 2019
%e 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.
%t Select[Range[1000], N[FractionalPart[Pi^#], 100] > 1 - (1/#) &] (* _G. C. Greubel_, Aug 25 2016 *)
%Y Cf. A153664, A153672, A153680, A153688, A153696, A153704, A153716, A154130, A153720.
%Y Cf. A001672.
%K nonn,more
%O 1,2
%A _Hieronymus Fischer_, Jan 06 2009
%E a(14) from _Robert Price_, Mar 25 2019
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