A002946 Continued fraction for cube root of 3. (Formerly M0408)

1, 2, 3, 1, 4, 1, 5, 1, 1, 6, 2, 5, 8, 3, 3, 4, 2, 6, 4, 4, 1, 3, 2, 3, 4, 1, 4, 9, 1, 8, 4, 3, 1, 3, 2, 6, 1, 6, 1, 3, 1, 1, 1, 1, 12, 3, 1, 3, 1, 1, 4, 1, 6, 1, 5, 1, 2, 1, 3, 3, 11, 8, 1, 139, 8, 2, 8, 5, 1, 2, 2, 2, 2, 3, 1, 1, 2, 1, 1, 1, 52, 2, 46, 2, 2, 3

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

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

3^(1/3) = 1.44224957030740838... = 1 + 1/(2 + 1/(3 + 1/(1 + 1/(4 + ...)))). - Harry J. Smith, May 08 2009

Maple

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

Mathematica

ContinuedFraction[Power[3, (3)^-1], 120] (* Harvey P. Dale, May 11 2011 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(3^(1/3)); for (n=1, 20000, write("b002946.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 08 2009
(Magma) SetDefaultRealField(RealField(100)); ContinuedFraction(3^(1/3)); // G. C. Greubel, Nov 02 2018

Crossrefs

Cf. A002581 (decimal expansion).

Cf. A002353, A002354 (convergents).

Sequence in context: A098554 A226081 A109201 * A286477 A277230 A218534

Adjacent sequences: A002943 A002944 A002945 * A002947 A002948 A002949

Keyword

nonn,cofr

Author

N. J. A. Sloane

Extensions

Offset changed by Andrew Howroyd, Jul 04 2024

Status

approved