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A295866
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Number of decimal digits in the number of partitions of n.
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0
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1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
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OFFSET
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0,7
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COMMENTS
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In his book on analytic number theory, Don Newman tells this amusing story regarding the number of digits in p(n): "This is told of Major MacMahon who kept a list of these partition numbers arranged one under another up into the hundreds. It suddenly occurred to him that, viewed from a distance, the outline of the digits seemed to form a parabola! Thus the number of digits in p(n), the number of partitions of n, is around C*sqrt(n), or p(n) itself is very roughly e^(a*sqrt(n)). The first crude assessment of p(n)!"
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REFERENCES
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D. J. Newman, Analytic number theory, Springer Verlag, 1998, p. 17.
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LINKS
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FORMULA
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MATHEMATICA
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Join[{1}, IntegerLength[PartitionsP[#]] & /@ Range[99]]
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PROG
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(PARI) a(n) = #digits(numbpart(n)); \\ Michel Marcus, Feb 17 2018
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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