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A334343
Continued fraction for Foias's constant (cf. A085848).
0
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
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
KEYWORD
nonn,cofr
AUTHOR
M. F. Hasler, Sep 07 2020
STATUS
approved