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Search: id:A059853
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| A059853 |
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Quotient cycle length of Sqrt(n^2+3). |
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+0
1
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| 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; listen)
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OFFSET
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2,1
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EXAMPLE
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If n=3k than a(n)=2, otherwise changing. 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]].
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MAPLE
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with(numtheory): [seq(nops(cfrac(sqrt(k^2+3), 'periodic', 'quotients')[2]), k=2..256)];
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CROSSREFS
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A002496, A005575, A056899, A049423, A056903.
Sequence in context: A129131 A097467 A092205 this_sequence A136527 A138614 A021705
Adjacent sequences: A059850 A059851 A059852 this_sequence A059854 A059855 A059856
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Feb 27 2001
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