A299616 Decimal expansion of e^(W(1) + W(2)) = 2/(W(1)*W(2)), where W is the Lambert W function (or PowerLog); see Comments.

4, 1, 3, 6, 0, 8, 1, 2, 9, 4, 7, 7, 8, 0, 1, 9, 9, 4, 3, 4, 2, 5, 8, 6, 5, 2, 2, 5, 7, 6, 0, 9, 1, 2, 5, 8, 4, 2, 1, 0, 1, 4, 8, 4, 5, 4, 0, 4, 1, 3, 0, 1, 4, 9, 5, 9, 2, 3, 9, 4, 5, 8, 0, 2, 7, 3, 6, 0, 4, 4, 9, 9, 9, 0, 6, 9, 6, 4, 1, 8, 0, 5, 4, 2, 7, 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(2)) = 2/(W(1)*W(2)). 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(2)) = 4.13608129477801994342...

Mathematica

w[x_] := ProductLog[x]; x = 1; y = 2; N[E^(w[x] + w[y]), 130]   (* A299616 *)
RealDigits[2/(LambertW[1]*LambertW[2]), 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)

Prog

(PARI) 2/(lambertw(1)*lambertw(2)) \\ G. C. Greubel, Mar 03 2018

Crossrefs

Cf. A299613, A299615.

Sequence in context: A090724 A343571 A308633 * A134224 A121441 A256243

Adjacent sequences: A299613 A299614 A299615 * A299617 A299618 A299619

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 01 2018

Status

approved