A299621 Decimal expansion of e^(W(1) + W(3)) = 3/(W(1)*W(3)), where W is the Lambert W function (or PowerLog); see Comments.

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

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(3)) = 3/(W(1)*W(3)). 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(3)) = 5.03821667615918674918541702644888...

Mathematica

w[x_] := ProductLog[x]; x = 1; y = 3;
N[E^(w[x] + w[y]), 130]   (* A299621 *)
RealDigits[3/(LambertW[1]*LambertW[3]), 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)

Prog

(PARI) 3/(lambertw(1)*lambertw(3)) \\ G. C. Greubel, Mar 03 2018

Crossrefs

Cf. A299613, A299620.

Sequence in context: A021669 A011511 A020856 * A182567 A339457 A300728

Adjacent sequences: A299618 A299619 A299620 * A299622 A299623 A299624

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 01 2018

Status

approved