A002354 Numerators of convergents to cube root of 3.

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: 0

Author

N. J. A. Sloane

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

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

Crossrefs

Cf. A002353 (denominators), A002581.

Programs

Mathematica

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

PARI

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

Extensions

More terms from Herman P. Robinson

More terms from Michel Marcus, Sep 08 2013

Offset changed by Andrew Howroyd, Jul 04 2024