A002948 Continued fraction for cube root of 5. (Formerly M0300)

1, 1, 2, 2, 4, 3, 3, 1, 5, 1, 1, 4, 10, 17, 1, 14, 1, 1, 3052, 1, 1, 1, 1, 1, 1, 2, 2, 1, 3, 2, 1, 13, 5, 1, 1, 1, 13, 2, 41, 1, 4, 12, 1, 5, 2, 7, 1, 1, 3, 33, 2, 1, 1, 1, 1, 1, 1, 3, 2, 2, 1, 15, 12

Offset

1,3

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 = 1..20000

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

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

Herman P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.

G. Xiao, Contfrac

Index entries for continued fractions for constants

Example

5^(1/3) = 1.70997594667669698... = 1 + 1/(1 + 1/(2 + 1/(2 + 1/(4 + ...)))). - Harry J. Smith, May 08 2009

Maple

with(numtheory): cfrac(5^(1/3), 80, 'quotients'); # Muniru A Asiru, Nov 02 2018

Mathematica

ContinuedFraction[5^(1/3), 100] (* G. C. Greubel, Nov 02 2018 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(5^(1/3)); for (n=1, 20000, write("b002948.txt", n, " ", x[n])); } \\ Harry J. Smith, May 08 2009
(Magma) SetDefaultRealField(RealField(100)); ContinuedFraction(5^(1/3)); // G. C. Greubel, Nov 02 2018

Crossrefs

Cf. A005481 = Decimal expansion. - Harry J. Smith, May 08 2009

Sequence in context: A094953 A332862 A122687 * A117113 A239430 A260951

Adjacent sequences: A002945 A002946 A002947 * A002949 A002950 A002951

Keyword

nonn,cofr

Author

N. J. A. Sloane

Status

approved