A002355 Denominators of convergents to cube root of 4.

1, 1, 2, 5, 12, 17, 63, 143, 492, 635, 2397, 3032, 93357, 96389, 478913, 575302, 1629517, 15240955, 93075247, 387541943, 480617190, 868159133, 2216935456, 16386707325, 34990350106, 121357757643, 277705865392, 399063623035, 2672087603602, 3071151226637

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

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

Crossrefs

Cf. A002356 (numerators), A005480.

Programs

Mathematica

Denominator[Convergents[Power[4, (3)^-1], 30]] (* Vincenzo Librandi, Aug 24 2013 *)

PARI

a(n) = contfracpnqn(contfrac(4^(1/3), n))[2, 1]; \\ Michel Marcus, Aug 23 2013

Extensions

More terms from Vincenzo Librandi, Aug 24 2013

Offset changed by Andrew Howroyd, Jul 04 2024