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A299621
Decimal expansion of e^(W(1) + W(3)) = 3/(W(1)*W(3)), where W is the Lambert W function (or PowerLog); see Comments.
3
5, 0, 3, 8, 2, 1, 6, 6, 7, 6, 1, 5, 9, 1, 8, 6, 7, 4, 9, 1, 8, 5, 4, 1, 7, 0, 2, 6, 4, 4, 8, 8, 8, 9, 4, 7, 1, 0, 8, 3, 7, 5, 9, 2, 2, 3, 9, 0, 2, 8, 1, 5, 6, 9, 3, 4, 4, 7, 2, 2, 9, 7, 1, 7, 9, 1, 2, 6, 5, 4, 4, 1, 0, 1, 3, 2, 6, 6, 9, 2, 1, 8, 5, 9, 4, 7
OFFSET
1,1
COMMENTS
The Lambert W function satisfies the functional equation e^(W(x) + W(y)) = x*y/(W(x)*W(y)) for x and y greater than -1/e, so that e^(W(1) + W(3)) = 3/(W(1)*W(3)). See A299613 for a guide to related constants.
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function
EXAMPLE
e^(W(1) + W(3)) = 5.03821667615918674918541702644888...
MATHEMATICA
w[x_] := ProductLog[x]; x = 1; y = 3;
N[E^(w[x] + w[y]), 130] (* A299621 *)
RealDigits[3/(LambertW[1]*LambertW[3]), 10, 100][[1]] (* G. C. Greubel, Mar 03 2018 *)
PROG
(PARI) 3/(lambertw(1)*lambertw(3)) \\ G. C. Greubel, Mar 03 2018
CROSSREFS
Sequence in context: A021669 A011511 A020856 * A182567 A339457 A300728
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Mar 01 2018
STATUS
approved