A002951 Continued fraction for fifth root of 5. (Formerly M0059)

1, 2, 1, 1, 1, 2, 1, 2, 8, 1, 25, 1, 5, 1, 22, 1, 8, 1, 1, 9, 1, 1, 4, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 6, 2, 46, 1, 12, 1, 32, 1, 2, 3, 2, 3, 55, 1, 12, 3, 8, 1, 1, 11, 1, 4, 1, 1, 1, 2, 1, 1, 7, 1, 1, 4, 3, 3, 3218, 1, 3, 1, 2, 2, 3, 1, 1, 2, 11, 1, 7, 57, 2, 2, 2, 2, 1, 1, 67, 1, 2, 3, 1, 1, 13, 3

Offset

0,2

Comments

Fifth root of 5 = 5^(1/5). - Harry J. Smith, May 10 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

Example

1.379729661461214832390063464... = 1 + 1/(2 + 1/(1 + 1/(1 + 1/(1 + ...)))). - Harry J. Smith, May 10 2009

Maple

with(numtheory): cfrac(5^(1/5), 100, 'quotients'); # Muniru A Asiru, Nov 02 2018

Mathematica

ContinuedFraction[5^(1/5), 100] (* G. C. Greubel, Nov 02 2018 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(5^(1/5)); for (n=1, 20000, write("b002951.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 10 2009
(Magma) SetDefaultRealField(RealField(100)); ContinuedFraction(5^(1/5)); // G. C. Greubel, Nov 02 2018

Crossrefs

Cf. A005534 (decimal expansion).

Cf. A002363, A002364 (convergents).

Sequence in context: A241597 A374164 A165194 * A331287 A365105 A093993

Adjacent sequences: A002948 A002949 A002950 * A002952 A002953 A002954

Keyword

nonn,cofr

Author

N. J. A. Sloane

Extensions

More terms copied from Smith's b-file by Hagen von Eitzen, Jul 20 2009

Offset changed by Andrew Howroyd, Jul 05 2024

Status

approved