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 A031144 #34 Feb 17 2018 10:29:21 %S A031144 0,5,7,12,18,19,20,22,25,28,34,37,38,50,57,61,73,85,94,105,114,115, %T A031144 122,124,127,133,153,154,162,172,176,182,185,186,194,203,213,216,241, %U A031144 249,254,257,264,273,285,304,327,337,345,353,357,394,395,402,420,425,426 %N A031144 Numbers n such that n! has a record number of zeros. %C A031144 All zeros are counted, not just the trailing zeros. So a particular n! might have more zeros than (n - 1)! (e.g., n = 10), but that's not enough for it to be in the sequence. - _Alonso del Arte_, Apr 30 2017 %H A031144 David A. Corneth, <a href="/A031144/b031144.txt">Table of n, a(n) for n = 1..476</a> %e A031144 Since 0! = 1, 0! has no significant zeros, and so 0 is the first term of the sequence. %e A031144 It isn't until 5! = 120 that n! gets its first significant zero, so 5 is the second term of the sequence. %t A031144 Function[s, -1 + Map[First@ Position[s, #] &, Union@ FoldList[Max, s]]]@ Array[DigitCount[#!, 10, 0] &, 430, 0] // Flatten (* _Michael De Vlieger_, May 12 2017 *) %o A031144 (PARI) lista(n) = my(l = List([0]), m=0, p=1, d); for(i=2,n, p*=i; d = digits(p); s = sum(i=1, #d, d[i]==0); if(s > m, listput(l, i); m=s));l \\ _David A. Corneth_, May 19 2017 %Y A031144 Cf. A031145. %K A031144 nonn,base,easy %O A031144 1,2 %A A031144 _N. J. A. Sloane_ %E A031144 Corrected and extended by _Erich Friedman_. %E A031144 Name clarified by _Alonso del Arte_, Apr 30 2017 %E A031144 Offset changed by _N. J. A. Sloane_, May 20 2017