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

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

Author

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

Keywords

• nonn
• 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

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

Crossrefs

Cf. A002359 (denominators), A002949, A005486.

Programs

Mathematica

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

PARI

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

Extensions

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

Offset changed by Andrew Howroyd, Jul 05 2024