A002946 Continued fraction for cube root of 3.

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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr

Examples

			3^(1/3) = 1.44224957030740838... = 1 + 1/(2 + 1/(3 + 1/(1 + 1/(4 + ...)))). - _Harry J. Smith_, May 08 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
• 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

Crossrefs

Cf. A002581 (decimal expansion).

Cf. A002353, A002354 (convergents).

Programs

Magma

SetDefaultRealField(RealField(100)); ContinuedFraction(3^(1/3)); // G. C. Greubel, Nov 02 2018

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 *)

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

Extensions

Offset changed by Andrew Howroyd, Jul 04 2024