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A242071 Decimal expansion of 'beta', a constant appearing in the random links Traveling Salesman Problem. 0
2, 0, 4, 1, 5, 4, 8, 1, 8, 6, 4, 1, 2, 1, 3, 2, 4, 1, 8, 0, 4, 5, 4, 9, 0, 1, 5, 8, 3, 8, 1, 4, 5, 5, 8, 6, 6, 3, 4, 0, 2, 5, 0, 2, 5, 2, 5, 6, 4, 6, 9, 1, 9, 1, 5, 5, 1, 2, 1, 3, 1, 2, 8, 1, 0, 5, 3, 6, 2, 1, 0, 6, 3, 7, 6, 7, 0, 0, 1, 2, 0, 9, 7, 1, 1, 0, 5, 5, 6, 4, 3, 9, 7, 6, 4, 3, 2, 8, 6, 9, 5, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.5 Traveling Salesman constants, p. 499.

LINKS

Table of n, a(n) for n=1..102.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 60.

FORMULA

beta = integral_{x>0} y(x) dx, where y(x) = -2 - W_(-1) (e^(-2-x) *(2-2*e^x+x)), W_k(z) being the k-th order Lambert W function (also known as ProductLog).  y(x) is implicitly defined by the equation (1+x/2)*exp(-x)+(1+y(x)/2)*exp(-y(x)) = 1.

EXAMPLE

2.041548186412132418045490158381455866340250252564691915512131281...

MATHEMATICA

y[x_] := -2 - ProductLog[-1, E^(-2-x)*(2 - 2*E^x + x)]; beta = (1/2)*NIntegrate[y[x], {x, 0, Infinity}, WorkingPrecision -> 102]; beta // RealDigits // First

CROSSREFS

Cf. A073008, A091505, A240717.

Sequence in context: A327883 A007432 A079124 * A176910 A243981 A056737

Adjacent sequences:  A242068 A242069 A242070 * A242072 A242073 A242074

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Aug 14 2014

STATUS

approved

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Last modified August 4 09:03 EDT 2020. Contains 336201 sequences. (Running on oeis4.)