A299618 Decimal expansion of W(1) + W(1/e), where w is the Lambert W function (or PowerLog); see Comments.

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

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 W(1) + W(1/e) = W((1/e)(1/W(1)) + 1/W(1/e))) = - 1 - log(W(1)) - log(W(1/e)). 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

W(1) + W(1/e) = 0.845607833170857668109327401233335...

Mathematica

w[x_] := ProductLog[x]; x = 1; y = 1/E; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]]  (* A299618 *)
RealDigits[LambertW[1] + LambertW[1/E], 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)

Prog

(PARI) lambertw(1) + lambertw(exp(-1)) \\ G. C. Greubel, Mar 03 2018

Crossrefs

Cf. A299613, A299619.

Sequence in context: A328017 A195431 A273635 * A021926 A254067 A178727

Adjacent sequences: A299615 A299616 A299617 * A299619 A299620 A299621

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 01 2018

Status

approved