A299615 Decimal expansion of W(1) + W(2), where w is the Lambert W function (or PowerLog); see Comments.

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

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(2) = W(2/W(1) + 2/W(2)) = log(2) - log(W(1)) - log(W(2)). 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(2) = 1.41974879242350936434644...

Mathematica

w[x_] := ProductLog[x]; x = 1; y = 2; u = N[w[x] + w[y], 100]
RealDigits[u, 10][[1]]  (* A299615 *)
RealDigits[LambertW[1] + LambertW[2], 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)

Prog

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

Crossrefs

Cf. A299613, A299616.

Sequence in context: A092162 A073056 A235944 * A353770 A049762 A105495

Adjacent sequences: A299612 A299613 A299614 * A299616 A299617 A299618

Keyword

nonn,cons,easy

Author

Clark Kimberling, Mar 01 2018

Status

approved