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A059855 Quotient cycle lengths in continued fraction expansion of sqrt(n^2+4). 0
1, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..100.

EXAMPLE

For even numbers 2, for odds 5 is the length of cycles: n=96,97 the integer parts and cycles are: [96],[48,192]] and [97],[48, 1, 1, 48, 194] resp. Inside cycles floor(n/2),1,1 and 2n arise.

MAPLE

with(numtheory): [seq(nops(cfrac(sqrt(k^2+4), 'periodic', 'quotients')[2]), k=1..100)];

MATHEMATICA

a[n_] := Length @ ContinuedFraction[Sqrt[n^2 + 4]][[2]]; Array[a, 100] (* Amiram Eldar, May 13 2020 *)

CROSSREFS

Cf. A002496, A005574, A056899, A049423, A056903, A056905.

Sequence in context: A073054 A010695 A021400 * A082881 A104289 A309697

Adjacent sequences:  A059852 A059853 A059854 * A059856 A059857 A059858

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 27 2001

STATUS

approved

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Last modified August 11 19:16 EDT 2020. Contains 336428 sequences. (Running on oeis4.)