Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Aug 26 2016 04:19:22
%S 1,2,23,24,35,41,65,182,72506,107346
%N Numbers k such that the fractional part of (Pi-2)^k is less than 1/k.
%C Numbers k such that fract((Pi-2)^k) < 1/k, where fract(x) = x-floor(x).
%C The next such number must be greater than 200000.
%C a(11) > 10^6. - _Jon E. Schoenfield_, Nov 15 2014
%e a(3)=23 since fract((Pi-2)^23) = 0.0260069... < 1/23, but fract((Pi-2)^k) >= 1/k for 3 <= k <= 22.
%t Select[Range[1000], N[FractionalPart[(Pi - 2)^#], 100] < (1/#) &] (* _G. C. Greubel_, Aug 25 2016 *)
%o (PARI) lista(nn) = for (n=1, nn, default(realprecision, n); if (frac((Pi-2)^n) < 1/n, print1(n, ", "))); \\ _Michel Marcus_, Nov 16 2014
%Y Cf. A153662, A153670, A153678, A153686, A153694, A153702, A153710, A153722, A154130.
%K nonn,more
%O 1,2
%A _Hieronymus Fischer_, Jan 06 2009