A243533 Decimal expansion of 'c', an asymptotic constant related to a variation of the "Secretary problem" with a uniform distribution.

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

Offset

1,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15 Optimal stopping constants, p. 362.

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's MathWorld, Sultan's Dowry Problem.

Wikipedia, Secretary problem.

Formula

log(A242672).

2*Sum_{k >= 3}(log(k)/(k^2-1)) - log(2)/3.

Example

1.3531302722959332816529440324922596269...

Mathematica

digits = 65; c = 2*NSum[Log[k]/(k^2 - 1), {k, 3, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 10^4, Method -> {"EulerMaclaurin", Method -> {"NIntegrate", "MaxRecursion" -> 10, Method -> "DoubleExponential"}}] - (Log[2]/3); RealDigits[c, 10, digits] // First

Crossrefs

Cf. A054404, A242672.

Sequence in context: A351179 A076824 A103728 * A239730 A287765 A162777

Adjacent sequences: A243530 A243531 A243532 * A243534 A243535 A243536

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 06 2014

Status

approved