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%I #10 Sep 03 2016 17:07:21
%S 1,2,8,39,113,3895,4714,8592,34289,60097,942859,2759790,6649343,
%T 7937397,14480816,19338413,19338414,19338415,23187701,124679421
%N Numbers k such that the fractional part of (4/3)^k is greater than 1-(1/k).
%C Numbers k such that fract((4/3)^k) > 1-(1/k), where fract(x) = x - floor(x).
%C The next term is greater than 3*10^8.
%e a(4) = 39, since fract((4/3)^39) = 0.9991861450... > 0.974358... = 1 - (1/39), but fract((4/3)^k) <= 1 - (1/k) for 8 < k < 39.
%t Select[Range[5000], N[FractionalPart[(4/3)^#], 100] > 1 - (1/#) &] (* _G. C. Greubel_, Sep 02 2016 *)
%o (PARI) isok(n) = frac((4/3)^n) > 1 - 1/n; \\ _Michel Marcus_, Sep 03 2016
%Y Cf. A153664, A153672, A153704, A153711, A154141, A154149.
%Y Cf. A002379, A064628.
%K nonn,more
%O 1,2
%A _Hieronymus Fischer_, Jan 11 2009
%E a(11)-a(20) from _Robert Gerbicz_, Nov 21 2010
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