A247847 Decimal expansion of m = (1-1/e^2)/2, one of Renyi's parking constants.

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

Offset

0,1

Comments

Curiously, this Renyi parking constant is very close to the prime generated continued fraction A084255 (gap ~ 10^-7).

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.3 Renyi's parking constant, p. 280.

Links

Table of n, a(n) for n=0..103.

Eric Weisstein's MathWorld, Rényi's Parking Constants

Marek Wolf, Continued fractions constructed from prime numbers, arxiv.org/abs/1003.4015, pp. 4-5.

Formula

Define s(n) = Sum_{k = 0..n} 2^k/k!. Then (1 - 1/e^2)/2 = Sum_{n >= 0} 2^n/( (n+1)!*s(n)*s(n+1) ). Cf. A073333. - Peter Bala, Oct 23 2023

Example

0.432332358381693654053000252513757798296184227045212...

Mathematica

RealDigits[(1 - 1/E^2)/2 , 10, 104] // First

Crossrefs

Cf. A001113, A050996, A073333, A084255, A092555, A242943, A243266, A247392.

Sequence in context: A248912 A152062 A084255 * A076576 A332558 A183197

Adjacent sequences: A247844 A247845 A247846 * A247848 A247849 A247850

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 25 2014

Status

approved