A003117 Continued fraction for fifth root of 3.

1, 4, 14, 2, 1, 1, 3, 2, 29, 2, 1, 7, 1, 5, 2, 1, 1, 19, 12, 77, 2, 16, 2, 1, 1, 15, 1, 1, 3, 14, 5, 1, 3, 2, 1, 1, 1, 1, 1, 1, 5, 1, 463, 1, 379, 3, 5, 3, 11, 1, 7, 7, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 46, 17, 44, 1, 1, 1, 2, 24, 9, 1, 7, 4, 1, 2, 2, 1, 3, 2, 7, 1, 7, 1, 1, 2, 1, 1, 4, 1, 46, 8, 2

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr

Examples

			1.24573093961551732596668033... = 1 + 1/(4 + 1/(14 + 1/(2 + 1/(1 + ...)))). - _Harry J. Smith_, May 12 2009
		

References

• H. P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Harry J. Smith, Table of n, a(n) for n = 0..19999
• Herman P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.
• J. Shallit & N. J. A. Sloane, Correspondence 1974-1975
• G. Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A005532 (decimal expansion).

Programs

Mathematica

ContinuedFraction[Surd[3,5],120] (* Harvey P. Dale, Dec 15 2018 *)

PARI

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(3^(1/5)); for (n=1, 20000, write("b003117.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 12 2009

Extensions

More terms from James Sellers, Sep 08 2000

Offset changed by Andrew Howroyd, Jul 05 2024