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A059854 Quotient cycle length of Sqrt(n^2+5) from n=3,... 0
4, 6, 2, 3, 6, 8, 10, 2, 4, 9, 4, 14, 2, 16, 6, 12, 12, 2, 16, 22, 10, 24, 2, 24, 12, 24, 16, 2, 6, 26, 30, 26, 2, 7, 20, 12, 18, 2, 18, 11, 20, 64, 2, 20, 30, 19, 22, 2, 40, 20, 10, 50, 2, 10, 38, 74, 14, 2, 22, 64, 50, 72, 2, 48, 10, 30, 48, 2, 22, 51, 10, 36, 2, 34, 12, 47, 46, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Table of n, a(n) for n=3..80.

FORMULA

with(numtheory): [seq(nops(cfrac(sqrt(k^2+5), 'periodic', 'quotients')[2]), k=3..256)];

EXAMPLE

If n=5k than a(n)=2, otherwise changing. Cycles for n=13, 14, 15 and 16:[5, 4, 5, 26]], [5, 1, 1, 1, 2, 1, 8, 1, 2, 1, 1, 1, 5, 28]], [6, 30]], [6, 2, 3, 7, 1, 3, 1, 2, 1, 3, 1, 7, 3, 2, 6, 32]]

CROSSREFS

Cf. A002496, A005575, A056899, A049423, A056903.

Sequence in context: A106143 A255524 A077158 * A155991 A184083 A244993

Adjacent sequences:  A059851 A059852 A059853 * A059855 A059856 A059857

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 27 2001

STATUS

approved

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Last modified September 17 08:31 EDT 2019. Contains 327127 sequences. (Running on oeis4.)