OFFSET
0,3
COMMENTS
a(6) = 563 shows that x = -23/30 is a good approximation to the negative solution to 2^x = x^2.
EXAMPLE
0.76666469596212309311... = 0 + 1/(1 + 1/(3 + 1/(3 + 1/(1 + 1/(1 + 1/(563 + ...))))))
MATHEMATICA
ContinuedFraction[ProductLog[Log[Sqrt[2]]]/Log[Sqrt[2]], 100]
PROG
(PARI) default(realprecision, 100); contfrac(lambertw(log(sqrt(2)))/log(sqrt(2)))
CROSSREFS
KEYWORD
nonn,cofr
AUTHOR
Jianing Song, May 17 2021
STATUS
approved