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 A177901 Numbers n > 1 such that s(n) = sum_{k=2..n} log10(k) is closer to an integer than any smaller n. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS MATHEMATICA mx=1; s=0; Reap[Do[s=s+N[Log[10, n], 30]; d=Abs[Round[s]-s]; If[d

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