A002359 Denominators of continued fraction convergents to cube root of 6.

1, 1, 5, 11, 82, 257, 130638, 130895, 785113, 4056460, 4841573, 8898033, 13739606, 36377245, 50116851, 86494096, 2125975155, 2212469251, 4338444406, 6550913657, 23991185377, 78524469788, 2379725279017, 9597425585856, 98353981137577

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• frac

References

• 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).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..999

Crossrefs

Cf. A002360 (numerators), A002949, A005486.

Programs

Mathematica

Denominator[Convergents[Power[6, (3)^-1],30]] (* Harvey P. Dale, Nov 26 2011 *)

PARI

a(n) = contfracpnqn(contfrac(6^(1/3), n))[2, 1]; \\ Michel Marcus, Aug 23 2013

Extensions

More terms from Herman P. Robinson

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 08 2004

Definition clarified by Harvey P. Dale, Nov 26 2011

Offset changed by Andrew Howroyd, Jul 05 2024