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A299618 Decimal expansion of W(1) + W(1/e), where w is the Lambert W function (or PowerLog); see Comments. 3
8, 4, 5, 6, 0, 7, 8, 3, 3, 1, 7, 0, 8, 5, 7, 6, 6, 8, 1, 0, 9, 3, 2, 7, 4, 0, 1, 2, 3, 3, 3, 3, 5, 7, 0, 5, 1, 9, 3, 2, 9, 3, 2, 7, 5, 8, 0, 6, 2, 5, 8, 2, 7, 3, 5, 8, 8, 3, 0, 9, 1, 8, 4, 7, 5, 8, 0, 7, 5, 1, 6, 8, 5, 4, 6, 6, 3, 4, 4, 6, 4, 8, 8, 5, 2, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

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

EXAMPLE

W(1) + W(1/e) = 0.845607833170857668109327401233335...

MATHEMATICA

w[x_] := ProductLog[x]; x = 1; y = 1/E; u = N[w[x] + w[y], 100]

RealDigits[u, 10][[1]]  (* A299618 *)

RealDigits[LambertW[1] + LambertW[1/E], 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)

PROG

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

CROSSREFS

Cf. A299613, A299619.

Sequence in context: A328017 A195431 A273635 * A021926 A254067 A178727

Adjacent sequences:  A299615 A299616 A299617 * A299619 A299620 A299621

KEYWORD

nonn,cons,easy

AUTHOR

Clark Kimberling, Mar 01 2018

STATUS

approved

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Last modified October 17 21:17 EDT 2021. Contains 348065 sequences. (Running on oeis4.)