A192181 Continued fraction expansion of the smallest real root of x^7-7x+3.

-2, 1, 1, 3, 1, 86, 63, 1006, 2, 1, 3, 3, 2, 3, 1, 1, 2, 4, 2, 7, 1, 1, 1, 1, 4, 2, 2, 1, 8, 1, 9, 1, 1, 50, 1, 3, 1, 16, 2, 1, 76, 1, 3, 3, 1, 3, 2, 1, 7, 2, 1, 46, 2, 1, 5, 4, 1, 1, 2, 1, 1, 11, 1, 1, 1, 2, 2, 2, 2, 13, 4, 1, 7, 2, 1, 1, 2, 1, 1, 4, 3, 1, 1, 3, 5, 7, 21, 5, 2, 1, 3, 1, 5, 1, 8, 9, 4, 3, 1

Offset

0,1

Links

Table of n, a(n) for n=0..98.

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

-1.4443022027143747.. = -2+1/(1+1/(1+1/(3+1/(1+1/(86+...))))).

Maple

Digits := 150 ;
x := -1.44;
for i from 1 to 10 do x := evalf(x-(x^7-7*x+3)/(7*x^6-7)); numtheory[cfrac](x+2, 80, 'quotients') ; end do; # R. J. Mathar, Jun 27 2011

Crossrefs

Cf. A192182, A192183.

Sequence in context: A173937 A046223 A338398 * A073463 A183568 A291958

Adjacent sequences: A192178 A192179 A192180 * A192182 A192183 A192184

Keyword

sign,cofr

Author

N. J. A. Sloane, Jun 25 2011

Status

approved