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A246672
Decimal expansion of 'xi', an optimal stopping auxiliary constant associated with the two choice case.
1
2, 7, 9, 3, 9, 9, 7, 6, 5, 2, 6, 0, 1, 5, 5, 0, 7, 9, 6, 0, 9, 9, 0, 7, 1, 1, 4, 1, 3, 6, 6, 8, 5, 0, 4, 2, 5, 8, 0, 0, 8, 3, 9, 1, 1, 6, 6, 2, 7, 3, 4, 2, 1, 1, 6, 1, 3, 5, 1, 5, 9, 8, 3, 1, 5, 4, 4, 3, 6, 3, 6, 4, 8, 8, 8, 9, 2, 8, 6, 8, 3, 5, 6, 2, 1, 1, 7, 4, 5, 6, 8, 8, 4, 2, 9, 1, 3, 5, 6, 0, 3, 5
OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15 Optimal stopping constants, p. 361.
LINKS
David Assaf, Larry Goldstein, Ester Samuel-Cahn, Two choice optimal stopping.
Eric Weisstein's MathWorld, Sultan's Dowry Problem.
Wikipedia, Secretary problem.
FORMULA
Unique positive solution of (2/xi + 1)*log(xi/2 + 1) = 3/2.
EXAMPLE
2.79399765260155079609907114136685042580083911662734211613515983...
MATHEMATICA
xi /. FindRoot[(2/xi + 1)*Log[xi/2 + 1] == 3/2, {xi, 3}, WorkingPrecision -> 102] // RealDigits // First
CROSSREFS
Cf. A246673.
Sequence in context: A198122 A021362 A371803 * A011054 A276140 A130818
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved