A050996 Decimal expansion of Rényi's parking constant.

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

Offset

0,1

Comments

Named after the Hungarian mathematician Alfréd Rényi (1921-1970). - Amiram Eldar, Jun 24 2021

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.3, p. 278.

A. Rényi, On a one-dimensional problem concerning random space-filling, Publ. Math. Inst. Hung. Acad. Sci., Vol. 3 (1958), pp. 109-127.

Links

Table of n, a(n) for n=0..100.

George Marsaglia, Arif Zaman and John C. W. Marsaglia, Numerical solution of some classical differential-difference equations, Math. Comp., Vol. 53, No. 187 (1989), pp. 191-201.

Simon Plouffe, The Parking or Renyi constant. [broken link]

Simon Plouffe, The Parking or Renyi constant.

Antonín Slavík, De Bruijn's Short Route to Rényi's Parking Constant, Amer. Math. Monthly 131 (2024), pp. 831-841 (preprint).

Philipp O. Tsvetkov, Stoichiometry of irreversible ligand binding to a one-dimensional lattice, Scientific Reports, Springer Nature, Vol. 10 (2020), Article number: 21308.

Eric Weisstein's World of Mathematics, Rényi's Parking Constants.

Formula

Equals exp(-2*gamma) * Integral_{x>=0} exp(2*Ei(-x))/x^2 dx, where gamma is Euler's constant (A001620) and Ei(x) is the exponential integral. - Amiram Eldar, Jun 24 2021

Example

0.7475979202534114351787309438301781730247862640742283766042291634251678816...

Mathematica

digits = 101; c = NIntegrate[E^(-2*(EulerGamma + Gamma[0, t] + Log[t])), {t, 0, Infinity}, WorkingPrecision -> digits + 10, MaxRecursion -> 20]; RealDigits[c, 10, digits][[1]] (* Jean-François Alcover, Nov 05 2012, updated May 21 2016 *)

Crossrefs

Cf. A001620, A050994, A050995.

Sequence in context: A153186 A343628 A085469 * A085541 A133055 A303133

Adjacent sequences: A050993 A050994 A050995 * A050997 A050998 A050999

Keyword

nonn,cons

Author

Eric W. Weisstein

Status

approved