A003117 Continued fraction for fifth root of 3. (Formerly M3473)

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

0,2

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A005532 (decimal expansion).

Sequence in context: A182439 A182441 A107775 * A239465 A156985 A138229

Adjacent sequences: A003114 A003115 A003116 * A003118 A003119 A003120

Keyword

nonn,cofr

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Sep 08 2000

Offset changed by Andrew Howroyd, Jul 05 2024

Status

approved