This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A153696 #14 Mar 24 2019 14:38:14 %S A153696 1,6,13,17,5513,12746,126237,430116,477190,1295623,1319307,3596185, %T A153696 6109350 %N A153696 Numbers k such that the fractional part of (10/9)^k is greater than 1-(1/k). %C A153696 Numbers k such that fract((10/9)^k) > 1-(1/k), where fract(x) = x-floor(x). %C A153696 The next such number must be greater than 2*10^5. %C A153696 a(14) > 10^7. - _Robert Price_, Mar 24 2019 %e A153696 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 A153696 Select[Range[1000], FractionalPart[(10/9)^#] >= 1 - (1/#) &] (* _G. C. Greubel_, Aug 24 2016 *) %Y A153696 Cf. A153664, A153672, A153680, A153688, A153700, A154130, A153704, A153712, A153720. %K A153696 nonn,more %O A153696 1,2 %A A153696 _Hieronymus Fischer_, Jan 06 2009 %E A153696 a(8)-a(13) from _Hans Havermann_, Apr 04 2016