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A357923
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a(n) is the least number of terms in the sum S = 1/(n+1) + 1/(n+2) + 1/(n+3) + ... such that S > n.
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1
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1, 3, 17, 68, 242, 812, 2619, 8224, 25345, 77006, 231355, 688758, 2034965, 5973932, 17441201, 50678536, 146643235, 422769139, 1214857227, 3480786068, 9946872233, 28357093263, 80667175724, 229020154166, 649028530125, 1836242560272, 5187142333288, 14632132586005
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ ceiling(exp(n + digamma(1+n)) - (1/2) - n).
floor(digamma(a(n)+n+1) - digamma(n+1)) = n. (End)
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EXAMPLE
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For n=0, a single term suffices: S = 1/1 > n = 0.
For n=1, a(1) = 3 terms suffice: S = 1/2 + 1/3 + 1/4 > n = 1.
For n=2, a(3) = 17 terms suffice: S = 1/3 + ... + 1/19 > 2.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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