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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. 5
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random Mapping Statistics, p. 288.
LINKS
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.
FORMULA
Equals sqrt(Pi/2)*Integral_{x=0..1} exp(li(x)) dx, where li is the logarithmic integral function.
Equals A069998 * A084945. - Amiram Eldar, Aug 25 2020
EXAMPLE
0.78248160099165661501621518806291...
MATHEMATICA
lambda = Integrate[Exp[LogIntegral[x]], {x, 0, 1}]; N[lambda*Sqrt[Pi/2], 99] // RealDigits // First
CROSSREFS
Sequence in context: A088367 A196610 A198938 * A225449 A345412 A021565
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved

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Last modified March 28 13:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)