A299614 Decimal expansion of e^(2*A030178) = e^(2*W(1)) = (1/W(1))^2, where W is the Lambert W function (or PowerLog); see Comments.

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

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^(2*W(1)) = (W(1))^(-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^(2*W(1)) = 3.1089547635799361854809454054...

Mathematica

w[x_] := ProductLog[x]; x = 1; y = 1;
N[E^(w[x] + w[y]), 130]   (* A299614 *)
RealDigits[(1/LambertW[1])^2, 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)

Prog

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

Crossrefs

Cf. A299613.

Sequence in context: A360829 A078521 A194938 * A135871 A126178 A094753

Adjacent sequences: A299611 A299612 A299613 * A299615 A299616 A299617

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 01 2018

Status

approved