A299632 Decimal expansion of 2*W(e/2), where W is the Lambert W function (or PowerLog); see Comments.

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

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(3/2) =W(e^2/2)/(1/W(e/2)) = 2 - log(4) - 2 log(W(e/2)). See A299613 for a guide to related sequences.

Links

Table of n, a(n) for n=0..85.

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

Example

2*W(e/2) = 1.3701538843091878920564989610752603...

Mathematica

w[x_] := ProductLog[x]; x = E/2; y = E/2; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]]  (* A299632 *)

Prog

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

Crossrefs

Cf. A299613, A299632.

Sequence in context: A261873 A293525 A016617 * A249186 A118746 A181913

Adjacent sequences: A299629 A299630 A299631 * A299633 A299634 A299635

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 13 2018

Status

approved