

A299623


Decimal expansion of e^(W(1) + W(1/2)) = (1/2)/(W(1)*W(1/2)), where W is the Lambert W function (or PowerLog); see Comments.


3



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

1,1


COMMENTS

The Lambert W function satisfies the functional equation e^(W(x) + W(y)) = x*y/(W(x)*W(y)) for x and y greater than 1/e, so that e^(W(1) + W(1/2)) = (1/2)/(W(1)*W(1/2)). See A299613 for a guide to related constants.


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Lambert WFunction


EXAMPLE

e^(W(1) + W(1/2)) = 2.506474042663898899474485815318941717...


MATHEMATICA

w[x_] := ProductLog[x]; x = 1; y = 1/2;
N[E^(w[x] + w[y]), 130] (* A299623 *)
RealDigits[1/(2*LambertW[1]*LambertW[1/2]), 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)


PROG

(PARI) 1/(2*lambertw(1)*lambertw(1/2)) \\ G. C. Greubel, Mar 03 2018


CROSSREFS

Cf. A299613, A299622.
Sequence in context: A268886 A090625 A021403 * A290796 A019727 A011184
Adjacent sequences: A299620 A299621 A299622 * A299624 A299625 A299626


KEYWORD

nonn,cons,easy


AUTHOR

Clark Kimberling, Mar 03 2018


STATUS

approved



