A299617 Decimal expansion of e^(W(1) + W(e)) = e/(W(1)*W(e)), where W is the Lambert W function (or PowerLog); see Comments.

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

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^(W(1) + W(e)) = e/(W(1)*W(e)). 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^(W(1) + W(e)) = 4.7929365901428140257258473723821086015...

Mathematica

w[x_] := ProductLog[x]; x = 1; y = E;
N[E^(w[x] + w[y]), 130]   (* A299617 *)
RealDigits[E/(LambertW[1]*LambertW[E]), 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)

Prog

(PARI) exp(1)/(lambertw(1)*lambertw(exp(1))) \\ G. C. Greubel, Mar 03 2018

Crossrefs

Cf. A299613, A030178.

Sequence in context: A010299 A201413 A021680 * A201931 A201504 A159898

Adjacent sequences: A299614 A299615 A299616 * A299618 A299619 A299620

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 01 2018

Status

approved