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A031144
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Numbers n such that n! has a record number of zeros.
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2
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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
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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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PROG
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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
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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