A002949 Continued fraction for cube root of 6.

1, 1, 4, 2, 7, 3, 508, 1, 5, 5, 1, 1, 1, 2, 1, 1, 24, 1, 1, 1, 3, 3, 30, 4, 10, 158, 6, 1, 1, 2, 12, 1, 10, 1, 1, 3, 2, 1, 1, 89, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 7, 1, 2, 18, 1, 17, 2, 2, 10, 14, 3, 1, 2, 1, 2, 1, 5, 1, 1, 2, 26, 1, 4, 65, 1, 1, 1, 27, 1, 2, 1, 4

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr

Examples

			6^(1/3) = 1.81712059283213965... = 1 + 1/(1 + 1/(4 + 1/(2 + 1/(7 + ...)))). - _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
• 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

Crossrefs

Cf. A005486 (decimal expansion).

Cf. A002359, A002360 (convergents).

Programs

Magma

SetDefaultRealField(RealField(100)); ContinuedFraction(6^(1/3)); // G. C. Greubel, Nov 02 2018

Maple

with(numtheory):
cfrac(6^(1/3),100,'quotients'); # Muniru A Asiru, Nov 02 2018

Mathematica

ContinuedFraction[6^(1/3), 100] (* G. C. Greubel, Nov 02 2018 *)

PARI

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(6^(1/3)); for (n=1, 20000, write("b002949.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 08 2009

Extensions

Offset changed by Andrew Howroyd, Jul 05 2024