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A084945
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Decimal expansion of Golomb-Dickman constant.
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25
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6, 2, 4, 3, 2, 9, 9, 8, 8, 5, 4, 3, 5, 5, 0, 8, 7, 0, 9, 9, 2, 9, 3, 6, 3, 8, 3, 1, 0, 0, 8, 3, 7, 2, 4, 4, 1, 7, 9, 6, 4, 2, 6, 2, 0, 1, 8, 0, 5, 2, 9, 2, 8, 6, 9, 7, 3, 5, 5, 1, 9, 0, 2, 4, 9, 5, 6, 3, 8, 0, 8, 8, 8, 5, 5, 1, 1, 3, 2, 5, 4, 4, 6, 2, 4, 6, 0, 2, 7, 6, 1, 9, 5, 5, 3, 9, 8, 6, 8, 8, 6, 9
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OFFSET
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0,1
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COMMENTS
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The average number of digits in the largest prime factor of a random x-digit number is asymptotically x times this constant. - Charles R Greathouse IV, Jul 28 2015
Named after the American mathematician Solomon W. Golomb (1932 - 2016) and the Swedish actuary Karl Dickman (1861 - 1947). - Amiram Eldar, Aug 25 2020
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 284-287.
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LINKS
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Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 171.
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FORMULA
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Equals Integral_{x=0..1} exp(li(x)) dx, where li(x) is the logarithmic integral.
Equals Integral_{x=0..oo} exp(-x + Ei(-x)) dx, where Ei(x) is the exponential integral.
Equals Integral_{x=0..1} F(x/(1-x)) dx, where F(x) is the Dickman function. (End)
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EXAMPLE
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0.62432998854355087...
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MAPLE
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E1:= z-> int(exp(-t)/t, t=z..infinity):
lambda:= int(exp(-x-E1(x)), x=0..infinity):
s:= convert(evalf(lambda, 130), string):
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MATHEMATICA
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NIntegrate[Exp[LogIntegral[x]], {x, 0, 1}, WorkingPrecision->110, MaxRecursion->20]
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PROG
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(PARI) default(realprecision, 103);
limitnum(n->intnum(x=0, 1-1/n, exp(-eint1(-log(x))))) \\ Gheorghe Coserea, Sep 26 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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