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A299613 Decimal expansion of 2*W(1), where W is the Lambert W function (or PowerLog); see Comments. 21
1, 1, 3, 4, 2, 8, 6, 5, 8, 0, 8, 1, 9, 5, 6, 7, 7, 4, 5, 9, 9, 9, 9, 3, 7, 3, 2, 4, 4, 2, 0, 7, 1, 1, 0, 9, 9, 5, 0, 7, 6, 3, 1, 5, 7, 4, 3, 7, 3, 0, 2, 5, 0, 1, 6, 2, 7, 0, 2, 6, 2, 1, 5, 8, 4, 4, 6, 0, 9, 1, 5, 8, 6, 1, 7, 3, 3, 6, 9, 1, 3, 3, 3, 8, 6, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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) = W(2/W(1)) = -2*log(W(1)).

Guide to related constants:

--------------------------------------------

x        y      W(x) + W(y)  e^(W(x) + W(y))

--------------------------------------------

1        1        A299613        A299614

1        2        A299615        A299616

1        e        A030178        A299617

e        e        2 exactly      e^2 exactly

1        1/e      A299618        A299619

1        3        A299620        A299621

1        1/2      A299622        A299623

1/2      1/2      A126583        A099954

2        2        A299624        A299625

3        3        A299626        A299627

1/3      1/3      A299628        A299629

3/2      3/2      A299630        A299631

e/2      e/2      A299632        A299633

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

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

Index entries for sequences related to LambertW function

Index entries for transcendental numbers

FORMULA

Equals 2*A030178.

EXAMPLE

2*W(1) = 1.13428658081956774599993...

MATHEMATICA

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

RealDigits[u, 10][[1]]  (* A299613 *)

RealDigits[2 ProductLog[1], 10, 111][[1]] (* Robert G. Wilson v, Mar 02 2018 *)

PROG

(PARI) 2*lambertw(1) \\ G. C. Greubel, Mar 07 2018

CROSSREFS

Cf. A299614-A299633.

Sequence in context: A020502 A252896 A266562 * A066892 A143053 A220508

Adjacent sequences:  A299610 A299611 A299612 * A299614 A299615 A299616

KEYWORD

nonn,cons,easy

AUTHOR

Clark Kimberling, Mar 01 2018

STATUS

approved

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Last modified January 24 18:36 EST 2021. Contains 340411 sequences. (Running on oeis4.)