A192183 Continued fraction expansion of the largest real root of x^7-7x+3.

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, 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, 1, 3, 1, 1, 4, 2, 1, 230, 2, 16, 1, 1, 1, 1, 3, 1, 2

Offset

0,2

Links

Table of n, a(n) for n=0..79.

David G. Cantor, Paul H. Galyean and Horst G. Zimmer, A continued fraction algorithm for real algebraic numbers. Math. Comp. 26 (1972), 785-791.

Example

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

Maple

Digits := 120 ;
x := 1.2933448 ;
for i from 1 to 10 do
        x := evalf(x-(x^7-7*x+3)/(7*x^6-7));
        numtheory[cfrac](x, 80, 'quotients') ;
end do; # R. J. Mathar, Jun 27 2011

Crossrefs

Cf. A192181, A192182.

Sequence in context: A111241 A345055 A247501 * A133518 A120729 A205139

Adjacent sequences: A192180 A192181 A192182 * A192184 A192185 A192186

Keyword

nonn,cofr

Author

N. J. A. Sloane, Jun 25 2011

Status

approved