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A050996 Decimal expansion of Rényi's parking constant. 10
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Named after the Hungarian mathematician Alfréd Rényi (1921-1970). - Amiram Eldar, Jun 24 2021
REFERENCES
A. Rényi, On a one-dimensional problem concerning random space-filling, Publ. Math. Inst. Hung. Acad. Sci., Vol. 3 (1958), pp. 109-127.
LINKS
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]
Antonín Slavík, De Bruijn's Short Route to Rényi's Parking Constant, Univ. Karlova (Czechia, 2014). See p. 11.
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
Sequence in context: A153186 A343628 A085469 * A085541 A133055 A303133
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)