The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A039922

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A039922

Continued fraction for root of x^5 - x - 1.
(history; published version)

#18 by N. J. A. Sloane at Thu Jun 15 22:43:44 EDT 2017

STATUS

proposed

approved

#17 by Nathan Fox at Thu Jun 15 22:34:03 EDT 2017

STATUS

editing

proposed

#16 by Nathan Fox at Thu Jun 15 22:33:16 EDT 2017

LINKS

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]

STATUS

approved

editing

#15 by Jon E. Schoenfield at Sun Jan 03 02:27:22 EST 2016

STATUS

editing

approved

#14 by Jon E. Schoenfield at Sun Jan 03 02:27:20 EST 2016

NAME

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

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#13 by Joerg Arndt at Sun Aug 02 04:14:33 EDT 2015

STATUS

proposed

approved

#12 by Michel Marcus at Sun Aug 02 03:51:08 EDT 2015

STATUS

editing

proposed

#11 by Michel Marcus at Sun Aug 02 03:51:02 EDT 2015

REFERENCES

S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134.

LINKS

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.

EXAMPLE

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

STATUS

approved

editing

#10 by Charles R Greathouse IV at Mon Apr 14 12:15:37 EDT 2014

STATUS

editing

approved

#9 by Charles R Greathouse IV at Mon Apr 14 12:15:35 EDT 2014

LINKS

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

EXAMPLE

1.16730397826141868425604589... = 1 + 1/(5 + 1/(1 + 1/(42 + 1/(1 + ...)))) [From _Harry J. Smith_, May 03 2009]

PROG

(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])); } [From _\\ _Harry J. Smith_, May 03 2009]

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

CROSSREFS

Cf. A160155 Decimal expansion. [From Harry J. Smith, May 03 2009]

Cf. A160155 Decimal expansion.

STATUS

approved

editing