A002949 Continued fraction for cube root of 6. (Formerly M3202)

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

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

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

Example

6^(1/3) = 1.81712059283213965... = 1 + 1/(1 + 1/(4 + 1/(2 + 1/(7 + ...)))). - Harry J. Smith, May 08 2009

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 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(6^(1/3)); for (n=1, 20000, write("b002949.txt", n, " ", x[n])); } \\ Harry J. Smith, May 08 2009
(Magma) SetDefaultRealField(RealField(100)); ContinuedFraction(6^(1/3)); // G. C. Greubel, Nov 02 2018

Crossrefs

Cf. A005486 = Decimal expansion. - Harry J. Smith, May 08 2009

Sequence in context: A180076 A169756 A329796 * A197026 A334417 A195779

Adjacent sequences: A002946 A002947 A002948 * A002950 A002951 A002952

Keyword

nonn,cofr

Author

N. J. A. Sloane

Status

approved