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A344390
Continued fraction for A073084, the constant LambertW(log(sqrt(2)))/log(sqrt(2)).
0
0, 1, 3, 3, 1, 1, 563, 4, 24, 1, 1, 1, 1, 8, 1, 1, 2, 1, 1, 1, 3, 2, 3, 2, 1, 1, 2, 190, 1, 1, 2, 1, 1, 2, 1, 6, 11, 3, 1, 1, 1, 1, 2, 1, 2, 2, 1, 4, 1, 1, 65, 1, 1, 1, 11, 25, 1, 2, 2, 2, 3, 29, 2, 16, 2, 3, 17, 5, 3, 4, 1, 3, 3, 20, 3, 1, 1, 2, 1, 2, 2, 2, 1, 3, 105, 8, 17, 1, 5, 1
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
Cf. A073084.
Sequence in context: A173503 A338114 A100940 * A063421 A368339 A244328
KEYWORD
nonn,cofr
AUTHOR
Jianing Song, May 17 2021
STATUS
approved