A299624 Decimal expansion of 2*W(2), where W is the Lambert W function (or PowerLog); see Comments.

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

Offset

0,2

Comments

The Lambert W function satisfies the functional equations

W(x) + W(y) = W(x*y*(1/W(x) + 1/W(y))) = log(x*y)/(W(x)*W(y)) for x and y greater than -1/e, so that 2*W(2) = W(8/W(2)) = 2*(log(2) - log(W(2))). See A299613 for a guide to related sequences.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

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

Example

2*W(2) = 1.7052110040274509826929448293906349337...

Mathematica

w[x_] := ProductLog[x]; x = 2; y = 2; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]]  (* A299624 *)
RealDigits[2*LambertW[2], 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)

Prog

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

Crossrefs

Cf. A299613, A299625.

Sequence in context: A099737 A395467 A271177 * A033150 A064648 A116198

Adjacent sequences: A299621 A299622 A299623 * A299625 A299626 A299627

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 03 2018

Status

approved