login
A299633
Decimal expansion of e^(2*W(e/2)) = (e^2/4)/(W(e/2))^2, where W is the Lambert W function (or PowerLog); see Comments.
3
3, 9, 3, 5, 9, 5, 6, 3, 3, 0, 7, 9, 1, 3, 4, 8, 8, 1, 0, 0, 2, 1, 1, 9, 8, 8, 4, 8, 9, 7, 7, 7, 0, 0, 7, 1, 8, 2, 9, 0, 2, 6, 6, 4, 3, 5, 6, 9, 6, 1, 5, 7, 6, 1, 0, 7, 4, 6, 1, 1, 8, 7, 0, 6, 0, 4, 2, 6, 8, 2, 2, 7, 3, 4, 2, 1, 5, 2, 7, 8, 0, 7, 1, 4, 3, 4
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^(2*W(e/2)) = (e^2/4)/(W(e/2))^2. See A299613 for a guide to related constants.
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function
EXAMPLE
e^(2*W(e/2)) = 3.9359563307913488100211988489777007...
MATHEMATICA
w[x_] := ProductLog[x]; x = e/2; y = e/2; N[E^(w[x] + w[y]), 130] (* A299633 *)
PROG
(PARI) exp(2*lambertw(exp(1)/2)) \\ Altug Alkan, Mar 13 2018
CROSSREFS
Sequence in context: A072560 A290506 A303111 * A074959 A010632 A340036
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Mar 13 2018
STATUS
approved