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A247847
Decimal expansion of m = (1-1/e^2)/2, one of Renyi's parking constants.
2
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
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
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved