%I #14 Mar 24 2019 14:38:14

%S 1,6,13,17,5513,12746,126237,430116,477190,1295623,1319307,3596185,

%T 6109350

%N Numbers k such that the fractional part of (10/9)^k is greater than 1-(1/k).

%C Numbers k such that fract((10/9)^k) > 1-(1/k), where fract(x) = x-floor(x).

%C The next such number must be greater than 2*10^5.

%C a(14) > 10^7. - _Robert Price_, Mar 24 2019

%e a(3) = 13, since fract((10/9)^13) = 0.9341... > 0.923... = 1 - (1/13), but fract((10/9)^k) <= 1 - (1/k) for 1 < k < 13.

%t Select[Range[1000], FractionalPart[(10/9)^#] >= 1 - (1/#) &] (* _G. C. Greubel_, Aug 24 2016 *)

%Y Cf. A153664, A153672, A153680, A153688, A153700, A154130, A153704, A153712, A153720.

%K nonn,more

%O 1,2

%A _Hieronymus Fischer_, Jan 06 2009

%E a(8)-a(13) from _Hans Havermann_, Apr 04 2016