A299627 Decimal expansion of e^(2*W(3)) = 9/(W(3))^2, where W is the Lambert W function (or PowerLog); see Comments.

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

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^(2*W(3)) = 9/(W(3))^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 W-Function

Example

e^(2*W(3)) = 8.1646820897128405910938873711...

Mathematica

w[x_] := ProductLog[x]; x = 3; y = 3;
N[E^(w[x] + w[y]), 130]   (* A299627 *)
RealDigits[(3/LambertW[3])^2, 10, 100][[1]] (* G. C. Greubel, Mar 06 2018 *)

Prog

(PARI) (3/lambertw(3))^2 \\ G. C. Greubel, Mar 06 2018

Crossrefs

Cf. A299613, A299626.

Sequence in context: A033812 A019717 A007404 * A157697 A281785 A240982

Adjacent sequences: A299624 A299625 A299626 * A299628 A299629 A299630

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 03 2018

Status

approved