A244067 Decimal expansion of the Purdom-Williams constant, a constant related to the Golomb-Dickman constant and to the asymptotic evaluation of the expectation of a random function longest cycle length.
7, 8, 2, 4, 8, 1, 6, 0, 0, 9, 9, 1, 6, 5, 6, 6, 1, 5, 0, 1, 6, 2, 1, 5, 1, 8, 8, 0, 6, 2, 9, 1, 0, 2, 8, 6, 6, 4, 4, 3, 0, 2, 8, 2, 5, 6, 6, 9, 6, 2, 8, 5, 8, 2, 4, 4, 1, 3, 7, 9, 2, 0, 3, 1, 9, 1, 7, 8, 0, 7, 1, 0, 9, 3, 0, 4, 0, 7, 4, 7, 3, 9, 1, 6, 5, 6, 9, 8, 8, 5, 2, 7, 3, 1, 0, 0, 3, 2, 0
Offset: 0
Examples
0.78248160099165661501621518806291...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random Mapping Statistics, p. 288.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..2500
- Paul W. Purdom and John H. Williams, Cycle length in a random function, Transactions of the American Mathematical Society, Vol. 133, No. 2 (1968), pp. 547-551.
- Eric Weisstein's MathWorld, Golomb-Dickman Constant.
- Wikipedia, Golomb-Dickman constant.
Programs
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Mathematica
lambda = Integrate[Exp[LogIntegral[x]], {x, 0, 1}]; N[lambda*Sqrt[Pi/2], 99] // RealDigits // First
Formula
Equals sqrt(Pi/2)*Integral_{x=0..1} exp(li(x)) dx, where li is the logarithmic integral function.