A299620 Decimal expansion of W(1) + W(3), where w is the Lambert W function (or PowerLog); see Comments.

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

Offset

1,2

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(3) = W(3/W(1) + 3/W(3)) = log(3) - log(W(1)) - log(W(3)). See A299613 for a guide to related sequences.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Lambert W-Function.

Example

W(1) + W(3) = 1.6170521853738238329886657327632...

Mathematica

w[x_] := ProductLog[x]; x = 1; y = 3; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]]  (* A299620 *)
RealDigits[LambertW[1] + LambertW[3], 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)

Prog

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

Crossrefs

Cf. A299613, A299621.

Sequence in context: A366868 A127778 A076714 * A113811 A126168 A331970

Adjacent sequences: A299617 A299618 A299619 * A299621 A299622 A299623

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 01 2018

Status

approved