A244261 Decimal expansion of c = 2.4149..., a random mapping statistics constant such that the asymptotic expectation of the maximum rho length (graph diameter) in a random n-mapping is c*sqrt(n).

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

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random Mapping Statistics, p. 288.

P. Flajolet and A. M. Odlyzko, Random Mapping Statistics, Advances in Cryptology - EUROCRYPT '89, J.-J. Quisquater and J. Vandewalle (eds.), Lecture Notes in Computer Science, Springer Verlag, 1990, pp. 329-354.

Links

Table of n, a(n) for n=1..20.

Formula

I(x) = integral_(0..x) (exp(-y)/y)*(1 - exp(-2*(y/(exp(x - y) - 1)))) dy,

c = sqrt(Pi/2)*integral_(0..infinity) 1 - exp(Ei(-x) - I(x)) dx, where Ei is the exponential integral function.

Example

2.4149010237176162411...

Maple

evalf(sqrt(Pi/2)*Int(1 - exp(Ei(-x) - Int((exp(-y)/y)*(1 - exp(-2*(y/(exp(x - y) - 1)))), y=0..x)), x=0..infinity)); # Vaclav Kotesovec, Aug 12 2019

Mathematica

digits = 20; m0 = 100; dm = 10; I0[x_?NumericQ] := NIntegrate[(Exp[-y]/y)*(1 - Exp[-2*(y/(Exp[x - y] - 1))]), {y, 0, x}, WorkingPrecision -> digits+5]; Clear[f]; f[m_] := f[m] = Sqrt[Pi/2]* NIntegrate[1 - Exp[ExpIntegralEi[-x] - I0[x]], {x, 0, m}, WorkingPrecision -> digits+5]; f[m0]; f[m = m0 + dm]; While[RealDigits[f[m], 10, digits+5] != RealDigits[f[m - dm], 10, digits+5], Print["m = ", m]; m = m + dm]; RealDigits[f[m], 10, digits] // First

Crossrefs

Cf. A084945, A244067, A244258.

Sequence in context: A201774 A011029 A256696 * A361873 A085111 A181332

Adjacent sequences: A244258 A244259 A244260 * A244262 A244263 A244264

Keyword

nonn,cons,more

Author

Jean-François Alcover, Jun 24 2014

Status

approved