A039922 Continued fraction for root of x^5 - x - 1.

1, 5, 1, 42, 1, 3, 24, 2, 2, 1, 16, 1, 11, 1, 1, 2, 31, 1, 12, 5, 1, 7, 11, 1, 4, 1, 4, 2, 2, 3, 4, 2, 1, 1, 11, 1, 41, 12, 1, 8, 1, 1, 1, 1, 1, 9, 2, 1, 5, 4, 1, 25, 4, 6, 11, 1, 4, 1, 6, 1, 1, 1, 2, 2, 2, 4, 11, 1, 4, 1, 3, 2, 8, 1, 3, 3, 6, 21, 11, 2, 1, 1, 10, 2, 1, 3

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr

Examples

			1.16730397826141868425604589... = 1 + 1/(5 + 1/(1 + 1/(42 + 1/(1 + ...)))).
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000
• S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134.
• S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134. [Annotated scanned copy]
• G. Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A160155 Decimal expansion.

Programs

PARI

{ allocatemem(932245000); default(realprecision, 21000); x=NULL; p=x^5 - x - 1; rs=polroots(p); r=real(rs[1]); c=contfrac(r); for (n=1, 20001, write("b039922.txt", n-1, " ", c[n])); } \\ Harry J. Smith, May 03 2009

PARI

contfrac(polrootsreal(x^5-x-1)[1]) \\ Charles R Greathouse IV, Apr 14 2014