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 A153678 #16 Mar 03 2020 06:57:53 %S A153678 1,2,3,4,5,6,585,1164,1707,522271,3675376,3906074,9424094 %N A153678 Numbers k such that the fractional part of (1024/1000)^k is less than 1/k. %C A153678 Numbers k such that fract((1024/1000)^k) < 1/k, where fract(x) = x-floor(x). %C A153678 The next such number must be greater than 5*10^5. %C A153678 a(14) > 10^7. - _Robert Price_, Mar 16 2019 %e A153678 a(7) = 585 since fract((1024/1000)^585) = 0.00139... < 1/585, but fract((1024/1000)^k) >= 1/k for 7 <= k <= 584. %t A153678 Select[Range[2000], FractionalPart[(1024/1000)^#] < (1/#) &] (* _G. C. Greubel_, Aug 24 2016; corrected by _Robert Price_, Mar 16 2019 *) %o A153678 (PARI) isok(n) = frac((1024/1000)^n) < 1/n \\ _Michel Marcus_, Aug 06 2013 %Y A153678 Cf. A153662, A153670, A153682, A154130, A153686, A153694, A153702, A153710, A153718. %K A153678 nonn,more %O A153678 1,2 %A A153678 _Hieronymus Fischer_, Jan 06 2009 %E A153678 a(10)-a(13) from _Robert Price_, Mar 16 2019