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
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
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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 *)
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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
Comments