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A059853 Quotient cycle length of sqrt(n^2+3). 0
4, 2, 6, 4, 2, 6, 10, 2, 12, 16, 2, 16, 20, 2, 10, 10, 2, 12, 10, 2, 28, 10, 2, 26, 16, 2, 18, 48, 2, 34, 12, 2, 26, 32, 2, 32, 32, 2, 20, 70, 2, 56, 34, 2, 24, 22, 2, 54, 52, 2, 70, 16, 2, 18, 38, 2, 16, 36, 2, 12, 72, 2, 114, 30, 2, 64, 32, 2, 52, 54, 2, 22, 92, 2, 154, 88, 2, 56 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Table of n, a(n) for n=2..79.

FORMULA

If n=3k than a(n)=2.

EXAMPLE

Integer parts and cycles for n=35, 36 and 37 are (with lengths=32, 2, 32): [[35], [23, 2, 1, 7, 8, 1, 1, 1, 2, 2, 1, 1, 5, 3, 1, 16, 1, 3, 5, 1, 1, 2, 2, 1, 1, 1, 8, 7, 1, 2, 23, 70]], [[36], [24, 72]] or [[37], [24, 1, 2, 7, 1, 8, 2, 1, 1, 1, 2, 2, 5, 1, 3, 18, 3, 1, 5, 2, 2, 1, 1, 1, 2, 8, 1, 7, 2, 1, 24, 74]].

MAPLE

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

CROSSREFS

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

Sequence in context: A242599 A092205 A272101 * A136527 A246776 A138614

Adjacent sequences:  A059850 A059851 A059852 * A059854 A059855 A059856

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 27 2001

STATUS

approved

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Last modified September 21 19:57 EDT 2020. Contains 337273 sequences. (Running on oeis4.)