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 A111683 #11 Apr 14 2015 16:46:56 %S A111683 2,3,40,5,576,11767,221824,168561,6371200,174442081,4680778752, %T A111683 4377478573,202076363776,7342081491375,260552186822656, %U A111683 226934809133761,14420591159943168,677361585374052121,30335097991823360000 %N A111683 n^k - n! where n^k > n! >= n^(k-1). %H A111683 Danny Rorabaugh, <a href="/A111683/b111683.txt">Table of n, a(n) for n = 2..447</a> %F A111683 a(n) = n^(1+floor(log_n(n!))) - n! = n^A060151(n) - A000142(n). - _Danny Rorabaugh_, Apr 14 2015 %e A111683 a(5) = 125 - 120 = 5, because 125 > 120 >= 25. %t A111683 For[n = 2, n < 20, n++, k := 0; While[n^k <= n!, k++ ]; Print[n^k - n! ]] (* _Stefan Steinerberger_, Jan 26 2006 *) %o A111683 (Sage) [n^(1+floor(log(factorial(n))/log(n))) - factorial(n) for n in range(2,21)] # _Danny Rorabaugh_, Apr 14 2015 %K A111683 nonn,easy %O A111683 2,1 %A A111683 _Amarnath Murthy_, Aug 16 2005 %E A111683 More terms from _Stefan Steinerberger_, Jan 26 2006