A084945 Decimal expansion of Golomb-Dickman constant.
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
Offset: 0
Examples
0.62432998854355087...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 284-287.
Links
- David Broadhurst, PrimeForm message on the first 1659 digits, Apr 02 2010.
- David Broadhurst, Titanic Golomb-Dickman prime, digest of 5 messages in primeform Yahoo group, Apr 2 - Apr 9, 2010. [Cached copy]
- Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 171.
- Solomon W. Golomb, Research Problem 11: Random permutations, Bull. Amer. Math. Soc. 70 (1964), p. 747.
- Jeffrey C. Lagarias, Euler's constant: Euler's work and modern developments, Bull. Amer. Math. Soc., Vol. 50, No. 4 (2013), pp. 527-628, preprint, arXiv:1303.1856 [math.NT], 2013.
- Andrew MacFie and Daniel Panario, Random Mappings with Restricted Preimages, in Progress in Cryptology-LATINCRYPT 2012, LNCS 7533, pp. 254-270, 2012. - From _N. J. A. Sloane_, Dec 25 2012
- Simon Plouffe, The Golomb constant.
- Eric Weisstein's World of Mathematics, Golomb-Dickman Constant.
- Wikipedia, Golomb-Dickman constant.
Programs
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Maple
E1:= z-> int(exp(-t)/t, t=z..infinity): lambda:= int(exp(-x-E1(x)), x=0..infinity): s:= convert(evalf(lambda, 130), string): seq(parse(s[n+1]), n=1..120); # Alois P. Heinz, Nov 20 2011
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Mathematica
NIntegrate[Exp[LogIntegral[x]], {x, 0, 1}, WorkingPrecision->110, MaxRecursion->20] -
PARI
intnum(x=0,1-1e-9,exp(-eint1(-log(x)))) \\ Charles R Greathouse IV, Jul 28 2015
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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
Formula
From Amiram Eldar, Aug 25 2020: (Start)
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)
Comments