A002359 -id:A002359 - cp's OEIS frontend

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

N. J. A. Sloane

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

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).

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

Cf. A005486 (decimal expansion).

Cf. A002359, A002360 (convergents).

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

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

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

{ 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

Offset changed by Andrew Howroyd, Jul 05 2024

A002360 Numerators of continued fraction convergents to cube root of 6.

Original entry on oeis.org

1, 2, 9, 20, 149, 467, 237385, 237852, 1426645, 7371077, 8797722, 16168799, 24966521, 66101841, 91068362, 157170203, 3863153234, 4020323437, 7883476671, 11903800108, 43594876995, 142688431093, 4324247809785, 17439679670233, 178721044512115, 28255364712584403

Offset: 0

N. J. A. Sloane, Herman P. Robinson

D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 67.
P. Seeling, Verwandlung der irrationalen Groesse ... in einen Kettenbruch, Archiv. Math. Phys., 46 (1866), 80-120.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Harvey P. Dale, Table of n, a(n) for n = 0..999

Cf. A002359 (denominators), A002949, A005486.

Numerator[Convergents[Power[6, (3)^-1],30]] (* Harvey P. Dale, Oct 16 2011 *)

a(n) = contfracpnqn(contfrac(6^(1/3), n))[1, 1]; \\ Michel Marcus, Aug 23 2013

Definition clarified by, and more terms from, Harvey P. Dale, Oct 16 2011

Offset changed by Andrew Howroyd, Jul 05 2024

cp's OEIS Frontend

A002949 Continued fraction for cube root of 6.

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