Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #34 Feb 17 2018 10:29:21
%S 0,5,7,12,18,19,20,22,25,28,34,37,38,50,57,61,73,85,94,105,114,115,
%T 122,124,127,133,153,154,162,172,176,182,185,186,194,203,213,216,241,
%U 249,254,257,264,273,285,304,327,337,345,353,357,394,395,402,420,425,426
%N Numbers n such that n! has a record number of zeros.
%C 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 David A. Corneth, <a href="/A031144/b031144.txt">Table of n, a(n) for n = 1..476</a>
%e Since 0! = 1, 0! has no significant zeros, and so 0 is the first term of the sequence.
%e It isn't until 5! = 120 that n! gets its first significant zero, so 5 is the second term of the sequence.
%t 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 (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 Cf. A031145.
%K nonn,base,easy
%O 1,2
%A _N. J. A. Sloane_
%E Corrected and extended by _Erich Friedman_.
%E Name clarified by _Alonso del Arte_, Apr 30 2017
%E Offset changed by _N. J. A. Sloane_, May 20 2017