A002354 Numerators of convergents to cube root of 3. (Formerly M2830 N1140)

1, 3, 10, 13, 62, 75, 437, 512, 949, 6206, 13361, 73011, 597449, 1865358, 6193523, 26639450, 59472423, 383473988, 1593368375, 6756947488, 8350315863, 31807895077, 71966106017, 247706213128, 1062790958529, 1310497171657, 6304779645157, 58053513978070

Offset

1,2

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Mathematica

Numerator[Convergents[3^(1/3), 30]] (* Vincenzo Librandi, Sep 09 2013 *)

Prog

(PARI) a(n)= contfracpnqn(contfrac(3^(1/3), n))[1, 1];  \\ Michel Marcus, Sep 08 2013

Crossrefs

Cf. A002353, A002581.

Sequence in context: A041985 A081519 A041121 * A079943 A041865 A357628

Adjacent sequences: A002351 A002352 A002353 * A002355 A002356 A002357

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

More terms from Herman P. Robinson

More terms from Michel Marcus, Sep 08 2013

Status

approved