A344390 Continued fraction for A073084, the constant LambertW(log(sqrt(2)))/log(sqrt(2)).

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

Author

Jianing Song, May 17 2021

Keywords

• nonn
• cofr

Comments

a(6) = 563 shows that x = -23/30 is a good approximation to the negative solution to 2^x = x^2.

Examples

			0.76666469596212309311... = 0 + 1/(1 + 1/(3 + 1/(3 + 1/(1 + 1/(1 + 1/(563 + ...))))))
		

Crossrefs

Cf. A073084.

Programs

Mathematica

ContinuedFraction[ProductLog[Log[Sqrt[2]]]/Log[Sqrt[2]], 100]

PARI

default(realprecision, 100); contfrac(lambertw(log(sqrt(2)))/log(sqrt(2)))