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Numbers n such that the fractional part of (4/3)^n is less than 1/n.
1

%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