A002362 Numerators of continued fraction convergents to fifth root of 2.

1, 7, 8, 23, 31, 54, 85, 309, 7810, 8119, 40286, 128977, 427217, 3119496, 162641009, 165760505, 494162019, 1648246562, 3790655143, 58508073707, 120806802557, 300121678821, 1321293517841, 21440817964277, 44202929446395, 330861324089042, 375064253535437

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. A002361 (denominators), A002950, A005531.

Programs

Mathematica

Numerator[Convergents[2^(1/5), 30]] (* Vincenzo Librandi, Sep 08 2013 *)

PARI

a(n)= contfracpnqn(contfrac(2^(1/5), n+1))[1, 1]; \\ Michel Marcus, Sep 07 2013

Extensions

More terms from Herman P. Robinson

More terms from Michel Marcus, Sep 07 2013

a(26)-a(27) corrected by Vincenzo Librandi, Sep 08 2013

Offset changed by Andrew Howroyd, Jul 05 2024