%I #30 Jan 06 2024 17:53:12
%S 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,
%T 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,
%U 22,15,2,8,2,2,1,4,1,13,2,1,3,1,2,1,12,2,4,1,2
%N Continued fraction for Foias's constant (cf. A085848).
%H Allan Wechsler, in reply to Christopher Landauer et al., <a href="https://mailman.xmission.com/cgi-bin/mailman/private/math-fun/2020-September/035752.html">Interesting limit question</a> (only available to subscribers), math-fun mailing list, Sept. 4, 2020.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FoiasConstant.html">Foias Constant</a>.
%F 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*...)...)
%F = x_1 where x_n = 1/(x_{n+1}^(1/n) - 1).
%e 1 + 1/( 5 + 1/( 2 + 1/( 1 + 1/( 81 + 1/( 3 + 1/( 2 + 1/( 2 + 1/( 1 + 1/( 1 + ... )...) = 1.1874523511265010545954801583965193512156926815858603530101041261990...
%o (PARI) F(n=default(realprecision)\.44+33,c=2/n)={until(!n--,c=1/sqrtn(c,n)-1);1/c}
%o contfrac(F()) \\ or use F()=foias(default(realprecision)) from A085848
%Y Cf. A085848.
%K nonn,cofr
%O 0,2
%A _M. F. Hasler_, Sep 07 2020