A299621 - OEIS

A299621

Decimal expansion of e^(W(1) + W(3)) = 3/(W(1)*W(3)), where W is the Lambert W function (or PowerLog); see Comments.

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

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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(3)) = 3/(W(1)*W(3)). 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 W-Function

EXAMPLE

e^(W(1) + W(3)) = 5.03821667615918674918541702644888...

MATHEMATICA

w[x_] := ProductLog[x]; x = 1; y = 3;

N[E^(w[x] + w[y]), 130] (* A299621 *)

RealDigits[3/(LambertW[1]*LambertW[3]), 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)

PROG

(PARI) 3/(lambertw(1)*lambertw(3)) \\ G. C. Greubel, Mar 03 2018

CROSSREFS