A002363 Denominators of continued fraction convergents to fifth root of 5. (Formerly M0703 N0260)

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

0,2

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]

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 *)

Crossrefs

Numerators in A002364.

Cf. A002951, A005534.

Sequence in context: A135568 A103004 A102016 * A041457 A161468 A229040

Adjacent sequences: A002360 A002361 A002362 * A002364 A002365 A002366

Keyword

nonn,frac,changed

Author

N. J. A. Sloane

Extensions

More terms from Herman P. Robinson

More terms from Harvey P. Dale, Jul 16 2016

Offset changed by Andrew Howroyd, Jul 05 2024

Status

approved