A242673 Decimal expansion of the unique real solution of the equation Ei(x)-gamma-log(x) = 1, where Ei is the exponential integral function and gamma the Euler-Mascheroni constant.

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

Offset

0,1

Comments

This constant is an auxiliary constant used in computing the asymptotic probability of success in one of the Secretary problems.

References

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

Links

Table of n, a(n) for n=0..99.

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

Wikipedia, Secretary problem.

Example

0.804352262845637584654638587784070551...

Mathematica

a = x /. FindRoot[ExpIntegralEi[x] - EulerGamma - Log[x] == 1, {x, 1}, WorkingPrecision -> 105]; RealDigits[a, 10, 100] // First

Crossrefs

Cf. A054404, A242672, A242674.

Sequence in context: A019959 A200482 A073824 * A188935 A155528 A096152

Adjacent sequences: A242670 A242671 A242672 * A242674 A242675 A242676

Keyword

nonn,cons

Author

Jean-François Alcover, May 20 2014

Status

approved