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A242672
Decimal expansion of an optimal stopping constant related to the Secretary problem.
5
3, 8, 6, 9, 5, 1, 9, 2, 4, 1, 3, 9, 7, 9, 9, 9, 4, 9, 5, 6, 9, 4, 1, 6, 7, 2, 7, 8, 7, 7, 9, 0, 8, 3, 4, 3, 2, 1, 9, 4, 6, 0, 6, 4, 3, 2, 5, 1, 9, 6, 9, 3, 3, 4, 4, 0, 4, 3, 9, 6, 0, 8, 9, 1, 1, 7, 0, 5, 9, 6, 2, 9, 9, 7, 8, 9, 8, 0, 3, 1, 5, 6, 0, 7, 0, 3, 6, 0, 6, 6, 7, 6, 1, 8, 4, 9, 3, 0, 8, 7, 1, 9, 7, 5, 7, 5
OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15, p. 362.
LINKS
FORMULA
product_(k>0) (1+2/k)^(1/(k+1)).
Also equals exp(2*Sum_{k>=3} (log(k)/(k^2-1)) - log(2)/3).
EXAMPLE
3.869519241397999495694167278779...
MATHEMATICA
NProduct[(1+2/k)^(1/(k+1)), {k, 1, Infinity}, NProductFactors -> 1000, WorkingPrecision -> 48] // RealDigits[#, 10, 40]& // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
More terms from Alois P. Heinz, Jun 06 2014
STATUS
approved