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A153718 Numbers k such that the fractional part of (Pi-2)^k is less than 1/k. 7

%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

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