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
Examples
0.432332358381693654053000252513757798296184227045212...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.3 Renyi's parking constant, p. 280.
Links
- Eric Weisstein's MathWorld, Rényi's Parking Constants
- Marek Wolf, Continued fractions constructed from prime numbers, arxiv.org/abs/1003.4015, pp. 4-5.
Programs
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Mathematica
RealDigits[(1 - 1/E^2)/2 , 10, 104] // First
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
Comments