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Continued fraction expansion of the largest real root of x^7-7x+3.
2

%I #10 Oct 12 2017 10:53:02

%S 1,3,2,2,4,15,4,1,7,70,1,7,2,1,8,4,3,4,1,1,1,1,3,2,2,1,9,1,1,22,1,24,

%T 899,3,1,2,1,1,5,1,22,1,1,1,1,58,1,1,13,2,1,1,1,1,5,2,1,1,34,1,1,6,11,

%U 1,3,1,1,4,2,1,230,2,16,1,1,1,1,3,1,2

%N Continued fraction expansion of the largest real root of x^7-7x+3.

%H David G. Cantor, Paul H. Galyean and Horst G. Zimmer, <a href="http://dx.doi.org/10.1090/S0025-5718-1972-0330118-4">A continued fraction algorithm for real algebraic numbers</a>. Math. Comp. 26 (1972), 785-791.

%e 1.2933448535... = 1+1/(3+1/(2+1/(2+... ))).

%p Digits := 120 ;

%p x := 1.2933448 ;

%p for i from 1 to 10 do

%p x := evalf(x-(x^7-7*x+3)/(7*x^6-7));

%p numtheory[cfrac](x,80,'quotients') ;

%p end do; # _R. J. Mathar_, Jun 27 2011

%Y Cf. A192181, A192182.

%K nonn,cofr

%O 0,2

%A _N. J. A. Sloane_, Jun 25 2011