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Search: id:A059855
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| A059855 |
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Quotient cycle lengths in continued fraction expansion of Sqrt(n^2+4). |
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+0
1
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| 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; listen)
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OFFSET
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1,2
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FORMULA
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with(numtheory): [seq(nops(cfrac(sqrt(k^2+4), 'periodic', 'quotients')[2]), k=1..100)];
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EXAMPLE
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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.
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CROSSREFS
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A002496, A005574, A056899, A049423, A056903, A056905.
Sequence in context: A122581 A010695 A021400 this_sequence A082881 A104289 A087272
Adjacent sequences: A059852 A059853 A059854 this_sequence A059856 A059857 A059858
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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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