A002364 Numerators of continued fraction convergents to fifth root of 5.

1, 3, 4, 7, 11, 29, 40, 109, 912, 1021, 26437, 27458, 163727, 191185, 4369797, 4560982, 40857653, 45418635, 86276288, 821905227, 908181515, 1730086742, 7828528483, 9558615225, 26945758933, 36504374158, 99954507249, 136458881407, 372872270063, 882203421533

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

• R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]

Crossrefs

Cf. A002363 (denominators), A002951 A005534.

Programs

Mathematica

Numerator[Convergents[Surd[5,5],30]] (* Harvey P. Dale, Dec 06 2015 *)

Extensions

Definition clarified by and more terms from Harvey P. Dale, Dec 06 2015

Offset changed by Andrew Howroyd, Jul 05 2024