

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
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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

N. J. A. Sloane


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



