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 A031144 Numbers n such that n! has a record number of zeros. 2
 0, 5, 7, 12, 18, 19, 20, 22, 25, 28, 34, 37, 38, 50, 57, 61, 73, 85, 94, 105, 114, 115, 122, 124, 127, 133, 153, 154, 162, 172, 176, 182, 185, 186, 194, 203, 213, 216, 241, 249, 254, 257, 264, 273, 285, 304, 327, 337, 345, 353, 357, 394, 395, 402, 420, 425, 426 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS David A. Corneth, Table of n, a(n) for n = 1..476 EXAMPLE Since 0! = 1, 0! has no significant zeros, and so 0 is the first term of the sequence. It isn't until 5! = 120 that n! gets its first significant zero, so 5 is the second term of the sequence. MATHEMATICA Function[s, -1 + Map[First@ Position[s, #] &, Union@ FoldList[Max, s]]]@ Array[DigitCount[#!, 10, 0] &, 430, 0] // Flatten (* Michael De Vlieger, May 12 2017 *) PROG (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 CROSSREFS Cf. A031145. Sequence in context: A117140 A263536 A314311 * A314312 A160243 A247027 Adjacent sequences:  A031141 A031142 A031143 * A031145 A031146 A031147 KEYWORD nonn,base,easy AUTHOR EXTENSIONS Corrected and extended by Erich Friedman. Name clarified by Alonso del Arte, Apr 30 2017 Offset changed by N. J. A. Sloane, May 20 2017 STATUS approved

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Last modified January 26 20:33 EST 2020. Contains 331288 sequences. (Running on oeis4.)