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Numbers k such that the fractional part of (3/2)^k is greater than 1-(1/k).
21

%I #12 Aug 24 2016 12:29:08

%S 1,14,163,1256,2677,8093,49304,49305,158643,164000,835999,2242294,

%T 2242295,2242296,3965133,25380333,92600006,92600007,92600008,92600009,

%U 92600010,92600011,99267816,125040717,125040718

%N Numbers k such that the fractional part of (3/2)^k is greater than 1-(1/k).

%C Numbers k such that fract((3/2)^k) > 1-(1/k), where fract(x) = x-floor(x).

%C The next term is greater than 3*10^8.

%e a(2) = 14 since fract((3/2)^14) = 0.92926... > 0.92857... = 1 - (1/14), but fract((3/2)^k) <= 1 - (1/k) for 1<k<14.

%t Select[Range[1000], FractionalPart[(3/2)^#] >= 1 - (1/#) &] (* _G. C. Greubel_, Aug 24 2016 *)

%Y Cf. A002379, A081464, A153662, A153663, A153665, A153666, A153667, A153668.

%K nonn,more

%O 1,2

%A _Hieronymus Fischer_, Dec 31 2008

%E a(11)-a(25) from _Robert Gerbicz_, Nov 21 2010