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A177901
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Numbers n > 1 such that s(n) = sum_{k=2..n} log10(k) is closer to an integer than any smaller n.
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1
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2, 3, 5, 14, 22, 27, 35, 95, 96, 197, 261, 5935, 7399, 8998, 11671, 17411, 108965, 165535, 258335, 549545, 1542194, 2064173, 4146167, 4594140, 5814278, 9242360, 21603225, 28563732, 40700787, 54528830
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OFFSET
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1,1
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COMMENTS
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If the Kamenetsky formula (See A034886) for the number of digits in n! ever fails, it will be at some number in this sequence where s(n) and log10(2*pi*n)/2 + n*(log10(n/e)) are on opposite sides of an integer. For n > 1, s(n) cannot be an integer, otherwise n! = 10^m for some m, which is not possible because n! has all the primes up to n as factors, but 10^m has only two prime factors: 2 and 5.
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LINKS
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Table of n, a(n) for n=1..30.
Noam D. Elkies, A counterexample to Kamenetsky's formula for the number of digits in n-factorial.
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MATHEMATICA
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mx=1; s=0; Reap[Do[s=s+N[Log[10, n], 30]; d=Abs[Round[s]-s]; If[d<mx, mx=d; Sow[n]], {n, 2, 10000}]][[2, 1]]
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CROSSREFS
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Sequence in context: A173654 A126333 A039575 * A143743 A104870 A114411
Adjacent sequences: A177898 A177899 A177900 * A177902 A177903 A177904
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe, Dec 15 2010
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STATUS
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approved
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