A299626 Decimal expansion of 2*W(3), where W is the Lambert W function (or PowerLog); see Comments.

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

Offset

0,1

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(3) =W(18/W(3)) = 2*(log 3 - log(W(3)). 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

3*W(3) = 2.0998177899280799199773941411...

Mathematica

w[x_] := ProductLog[x]; x = 3; y = 3; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]]  (* A299626 *)
RealDigits[2*LambertW[3], 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)

Prog

(PARI) 2*lambertw(3) \\ G. C. Greubel, Mar 03 2018

Crossrefs

Cf. A299613, A299627.

Sequence in context: A083864 A154937 A037996 * A002741 A213322 A368703

Adjacent sequences: A299623 A299624 A299625 * A299627 A299628 A299629

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 03 2018

Status

approved