A002360 Numerators of continued fraction convergents to cube root of 6. (Formerly M1918 N0756)

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

0,2

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

Mathematica

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

Prog

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

Crossrefs

Cf. A002359 (denominators), A002949, A005486.

Sequence in context: A264294 A280295 A041007 * A100516 A337015 A041285

Adjacent sequences: A002357 A002358 A002359 * A002361 A002362 A002363

Keyword

nonn,frac,changed

Author

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

Extensions

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

Offset changed by Andrew Howroyd, Jul 05 2024

Status

approved