A005483 Continued fraction for cube root of 7.

1, 1, 10, 2, 16, 2, 1, 4, 2, 1, 21, 1, 3, 5, 1, 2, 1, 1, 2, 11, 5, 1, 3, 1, 2, 27, 4, 1, 282, 8, 1, 2, 1, 1, 3, 1, 3, 2, 6, 4, 1, 2, 1, 5, 1, 1, 2, 1, 1, 1, 3, 2, 8, 1, 2, 2, 4, 5, 1, 1, 36, 1, 1, 1, 1, 2, 1, 2, 31, 2, 1, 1, 7, 1, 1, 1, 1, 6, 7, 6, 5, 7, 1, 6, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr

Examples

			7^(1/3) = 1.912931182772389... = 1 + 1/(1 + 1/(10 + 1/(2 + 1/(16 + ...)))). - _Harry J. Smith_, May 08 2009
		

References

• 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]
• G. Xiao, Contfrac
• Index entries for continued fractions for constants

Crossrefs

Cf. A005482 (decimal expansion).

Cf. A005484, A005485 (convergents).

Programs

Mathematica

ContinuedFraction[Surd[7,3],70] (* Harvey P. Dale, Oct 01 2013 *)

PARI

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(7^(1/3)); for (n=1, 20000, write("b005483.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 08 2009

Extensions

Offset changed by Andrew Howroyd, Jul 05 2024