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

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

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

Examples

			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.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..476

Crossrefs

Cf. A031145.

Programs

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 *)

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

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