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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 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-François Alcover, Aug 14 2014 STATUS approved

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