A334343 Continued fraction for Foias's constant (cf. A085848).

1, 5, 2, 1, 81, 3, 2, 2, 1, 1, 1, 1, 1, 6, 1, 1, 3, 1, 1, 4, 3, 2, 5, 1, 2, 4, 1, 1, 5, 2, 2, 8, 9, 1, 6, 3, 2, 1, 1, 3, 1, 1, 2, 3, 4, 4, 1, 3, 1, 1, 1, 1, 3, 11, 1, 5, 2, 1, 1, 4, 1, 12, 31, 1, 2, 2, 22, 15, 2, 8, 2, 2, 1, 4, 1, 13, 2, 1, 3, 1, 2, 1, 12, 2, 4, 1, 2

Offset

0,2

Links

Table of n, a(n) for n=0..86.

Allan Wechsler, in reply to Christopher Landauer et al., Interesting limit question (only available to subscribers), math-fun mailing list, Sept. 4, 2020.

Eric Weisstein's World of Mathematics, Foias Constant.

Formula

1/(-1+1/(-1+exp(-1/2*log(abs(-1+exp(-1/3*log(abs(-1+exp(-1/4*log(abs(-1+exp(-1/5*...)...)

= x_1 where x_n = 1/(x_{n+1}^(1/n) - 1).

Example

1 + 1/( 5 + 1/( 2 + 1/( 1 + 1/( 81 + 1/( 3 + 1/( 2 + 1/( 2 + 1/( 1 + 1/( 1 + ... )...) = 1.1874523511265010545954801583965193512156926815858603530101041261990...

Prog

(PARI) F(n=default(realprecision)\.44+33, c=2/n)={until(!n--, c=1/sqrtn(c, n)-1); 1/c}
contfrac(F()) \\ or use F()=foias(default(realprecision)) from A085848

Crossrefs

Cf. A085848.

Sequence in context: A107719 A229959 A174485 * A285641 A257856 A021661

Adjacent sequences: A334340 A334341 A334342 * A334344 A334345 A334346

Keyword

nonn,cofr

Author

M. F. Hasler, Sep 07 2020

Status

approved