

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
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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 WFunction


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



