A242071 Decimal expansion of 'beta', a constant appearing in the random links Traveling Salesman Problem.

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

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: A007432 A079124 A390746 * A176910 A243981 A369657

Adjacent sequences: A242068 A242069 A242070 * A242072 A242073 A242074

Keyword

nonn,cons

Author

Jean-François Alcover, Aug 14 2014

Status

approved