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Search: id:A059927
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| A059927 |
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Quotient cycle length in continued fraction expansion of sqrt(2^(2n-1)), i.e. square root of odd power of 2, quadratic surds. |
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+0
3
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| 1, 2, 4, 4, 12, 24, 48, 96, 196, 368, 760, 1524, 3064, 6068, 12168, 24360, 48668, 97160, 194952, 389416, 778832, 1557780, 3116216, 6229836, 12462296, 24923320, 49849604, 99694536, 199394616, 398783628, 797556364, 1595117676, 3190297400, 6380517544, 12761088588, 25522110948
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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K. R. Matthews, On the continued fraction expansion of sqrt(2^(2n+1))
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EXAMPLE
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cfrac(sqrt(2048),'periodic','quotients')= [[45],[3,1,12,5,1,1,2,1,2,4,1,21,1,4,2,1,2,1,1,5,12,1,3,90]] the period of length 24 of 2^11 yielding a(6)=24.
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MAPLE
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with(numtheory): [seq(nops(cfrac(sqrt(2^(2*k-1)), 'periodic', 'quotients')[2]), k=1..15)];
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CROSSREFS
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Cf. A059866.
Sequence in context: A129882 A129017 A086915 this_sequence A089419 A077815 A064449
Adjacent sequences: A059924 A059925 A059926 this_sequence A059928 A059929 A059930
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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), Mar 01 2001
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EXTENSIONS
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More terms from Don Reble (djr(AT)nk.ca), Oct 31 2001
a(32)=3190297400 (Don Reble Feb 10, 2007)
a(33), a(34) and a(35) from Keith Matthews (keithmatt(AT)gmail.com), Feb 16 2007, Feb 28 2007
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