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A299628 Decimal expansion of 2*W(1/3), where W is the Lambert W function (or PowerLog); see Comments. 3
5, 1, 5, 2, 5, 5, 3, 0, 6, 0, 9, 9, 4, 7, 3, 4, 0, 8, 5, 6, 5, 8, 3, 2, 4, 0, 3, 2, 5, 2, 1, 9, 5, 5, 8, 1, 8, 1, 9, 3, 8, 5, 2, 9, 5, 0, 0, 6, 4, 0, 8, 9, 8, 3, 0, 6, 7, 9, 0, 2, 2, 8, 8, 1, 3, 2, 6, 3, 8, 2, 5, 8, 5, 5, 0, 4, 0, 8, 7, 4, 4, 9, 1, 9, 2, 7 (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 2*W(1/3) = W(2)/(9*W(1/3)) = -2*log(3) - 2*log(W(1/3)). 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

2*W(1/3) = 0.5152553060994734085658324032521955...

MATHEMATICA

w[x_] := ProductLog[x]; x = 1/3; y = 1/3; u = N[w[x] + w[y], 100]

RealDigits[u, 10][[1]]  (* A299628 *)

RealDigits[2*LambertW[1/3], 10, 100][[1]] (* G. C. Greubel, Mar 06 2018 *)

PROG

(PARI) 2*lambertw(1/3) \\ G. C. Greubel, Mar 06 2018

CROSSREFS

Cf. A299613, A299629.

Sequence in context: A050340 A021955 A055191 * A217774 A060186 A240995

Adjacent sequences:  A299625 A299626 A299627 * A299629 A299630 A299631

KEYWORD

nonn,cons,easy

AUTHOR

Clark Kimberling, Mar 03 2018

STATUS

approved

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Last modified January 20 23:24 EST 2020. Contains 331104 sequences. (Running on oeis4.)