A002363 Denominators of continued fraction convergents to fifth root of 5.

1, 2, 3, 5, 8, 21, 29, 79, 661, 740, 19161, 19901, 118666, 138567, 3167140, 3305707, 29612796, 32918503, 62531299, 595700194, 658231493, 1253931687, 5673958241, 6927889928, 19529738097, 26457628025, 72444994147, 98902622172, 270250238491, 639403099154

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

• Robert Israel, Table of n, a(n) for n = 0..1996
• R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]

Crossrefs

Numerators in A002364.

Cf. A002951, A005534.

Programs

Maple

numtheory:-cfrac(5^(1/5),1000,'con'):
map(denom,con); # Robert Israel, May 13 2018

Mathematica

Denominator[Convergents[Surd[5,5],30]] (* Harvey P. Dale, Jul 16 2016 *)

Extensions

More terms from Herman P. Robinson

More terms from Harvey P. Dale, Jul 16 2016

Offset changed by Andrew Howroyd, Jul 05 2024