A031144 Numbers n such that n! has a record number of zeros.

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

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 A373670 A160243

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