cp's OEIS Frontend

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.

%I A244067 #16 Feb 16 2025 08:33:22
%S A244067 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,
%T A244067 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,
%U A244067 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
%N 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.
%D A244067 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random Mapping Statistics, p. 288.
%H A244067 G. C. Greubel, <a href="/A244067/b244067.txt">Table of n, a(n) for n = 0..2500</a>
%H A244067 Paul W. Purdom and John H. Williams, <a href="https://doi.org/10.1090/S0002-9947-1968-0228032-3">Cycle length in a random function</a>, Transactions of the American Mathematical Society, Vol. 133, No. 2 (1968), pp. 547-551.
%H A244067 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/Golomb-DickmanConstant.html">Golomb-Dickman Constant</a>.
%H A244067 Wikipedia, <a href="http://en.wikipedia.org/wiki/Golomb%E2%80%93Dickman_constant">Golomb-Dickman constant</a>.
%F A244067 Equals sqrt(Pi/2)*Integral_{x=0..1} exp(li(x)) dx, where li is the logarithmic integral function.
%F A244067 Equals A069998 * A084945. - _Amiram Eldar_, Aug 25 2020
%e A244067 0.78248160099165661501621518806291...
%t A244067 lambda = Integrate[Exp[LogIntegral[x]], {x, 0, 1}]; N[lambda*Sqrt[Pi/2], 99] // RealDigits // First
%Y A244067 Cf. A069998, A084945.
%K A244067 nonn,cons,easy
%O A244067 0,1
%A A244067 _Jean-François Alcover_, Jun 19 2014