login
Continued fraction for root of x^5 - x - 1.
2

%I #18 Jun 15 2017 22:43:44

%S 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,

%T 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,

%U 2,2,4,11,1,4,1,3,2,8,1,3,3,6,21,11,2,1,1,10,2,1,3

%N Continued fraction for root of x^5 - x - 1.

%H Harry J. Smith, <a href="/A039922/b039922.txt">Table of n, a(n) for n = 0..20000</a>

%H S. Lang and H. Trotter, <a href="http://dx.doi.org/10.1515/crll.1972.255.112">Continued fractions for some algebraic numbers</a>, J. Reine Angew. Math. 255 (1972), 112-134.

%H S. Lang and H. Trotter, <a href="/A002945/a002945.pdf">Continued fractions for some algebraic numbers</a>, J. Reine Angew. Math. 255 (1972), 112-134. [Annotated scanned copy]

%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

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

%o (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

%o (PARI) contfrac(polrootsreal(x^5-x-1)[1]) \\ _Charles R Greathouse IV_, Apr 14 2014

%Y Cf. A160155 Decimal expansion.

%K nonn,cofr

%O 0,2

%A _N. J. A. Sloane_