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 A153688 #9 Mar 19 2019 11:27:44 %S A153688 1,7,77,103,320,1821,2992,15290,88651,88652,180168,410498,548816, %T A153688 672732 %N A153688 Numbers k such that the fractional part of (11/10)^k is greater than 1-(1/k). %C A153688 Numbers k such that fract((11/10)^k) > 1-(1/k), where fract(x) = x-floor(x). %C A153688 The next such number must be greater than 2*10^5. %C A153688 a(15) > 10^7. _Robert Price_, Mar 19 2019 %e A153688 a(2) = 7, since fract((11/10)^7) = 0.9487... > 0.8571... = 1 - (1/7), but fract((11/10)^k) <= 1 - (1/k) for 1 < k < 7. %t A153688 Select[Range[1000], FractionalPart[(11/10)^#] >= 1 - (1/#) &] (* _G. C. Greubel_, Aug 24 2016 *) %Y A153688 Cf. A153664, A153672, A153684, A153692, A154130, A153696, A153704, A153712, A153720. %K A153688 nonn,more %O A153688 1,2 %A A153688 _Hieronymus Fischer_, Jan 06 2009 %E A153688 a(12)-a(14) from _Robert Price_, Mar 19 2019