A242943 Decimal expansion of the mean car density associated with Solomon's variation in Renyi's one-dimensional parking problem.

8, 0, 8, 6, 5, 2, 5, 1, 8, 3, 5, 0, 2, 1, 2, 2, 4, 4, 9, 1, 5, 4, 2, 1, 9, 2, 9, 4, 0, 9, 6, 8, 0, 3, 2, 9, 4, 4, 1, 0, 8, 0, 1, 2, 4, 7, 1, 3, 8, 6, 9, 4, 8, 5, 4, 3, 2, 2, 5, 1, 2, 9, 6, 6, 5, 4, 1, 3, 2, 3, 3, 2, 7, 9, 2, 6, 9, 5, 3, 9, 1, 2, 7, 4, 5, 5, 1, 6, 0, 4, 9, 1, 0, 4, 7, 7, 8, 9, 1, 8, 7, 2

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.3 Renyi's parking constant, p. 279.

Links

Table of n, a(n) for n=0..101.

Eric Weisstein's MathWorld, Rényi's Parking Constants

Formula

integral_(x>=0) (2*x+1)*exp(-2*(x+exp(-x)-1)]*exp(-2*(-Ei(-x)+log(x)+gamma)) dx, where Ei is the exponential integral function and gamma the Euler-Mascheroni constant.

Example

0.808652518350212244915421929409680329441...

Mathematica

digits = 102; NIntegrate[(2*x + 1)*Exp[-2*(x + Exp[-x] - 1)]*Exp[-2*(-ExpIntegralEi[-x] + Log[x] + EulerGamma)], {x, 0, Infinity}, WorkingPrecision -> digits + 5] // RealDigits[#, 10, digits] & // First

Crossrefs

Cf. A050996.

Sequence in context: A156744 A228438 A021557 * A358941 A319215 A200513

Adjacent sequences: A242940 A242941 A242942 * A242944 A242945 A242946

Keyword

nonn,cons

Author

Jean-François Alcover, May 27 2014

Status

approved