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%I #11 Sep 03 2016 17:07:14
%S 1,4,17,1738,1739,12863,15705,109705,174894,289047,720429,2087694,
%T 2087695,4475944,6968999
%N Numbers n such that the fractional part of (4/3)^n is less than 1/n.
%C Numbers n such that fract((4/3)^n) < 1/n, where fract(x) = x - floor(x).
%C The next term is greater than 3*10^8.
%e a(3)=17 since fract((4/3)^17) = 0.03273... < 1/17, but fract((4/3)^k) >= 1/k for 5 <= k <= 16.
%t Select[Range[1000], N[FractionalPart[(4/3)^#], 100] < (1/#) &] (* _G. C. Greubel_, Sep 02 2016 *)
%o (PARI) isok(n) = frac((4/3)^n) < 1/n; \\ _Michel Marcus_, Sep 03 2016
%Y Cf. A153662, A153670, A153702, A137994, A154139, A154147.
%Y Cf. A002379, A064628.
%K nonn,more
%O 1,2
%A _Hieronymus Fischer_, Jan 11 2009
%E a(10)-a(15) from _Robert Gerbicz_, Nov 21 2010
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