A299629 Decimal expansion of e^(2*W(1/3)) = (1/9)/(W(1/3))^2, where W is the Lambert W function (or PowerLog); see Comments.

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

Offset

1,2

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^(2*W(1/3)) = (1/9)/(W(1/3))^2. See A299613 for a guide to related constants.

Links

Table of n, a(n) for n=1..86.

Eric Weisstein's World of Mathematics, Lambert W-Function

Example

e^(2*W(1/3)) = 1.674065846464880772226081114...

Mathematica

w[x_] := ProductLog[x]; x = 1/3; y = 1/3; N[E^(w[x] + w[y]), 130]   (* A299629 *)

Prog

(PARI) exp(2*lambertw(1/3)) \\ Altug Alkan, Mar 13 2018

Crossrefs

Cf. A299613, A299628.

Sequence in context: A049254 A144028 A089321 * A200308 A097410 A367312

Adjacent sequences: A299626 A299627 A299628 * A299630 A299631 A299632

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 13 2018

Status

approved