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Search: id:A059926
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| A059926 |
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Quotient cycle length in continued fraction expansion of sqrt(2^n+1). |
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+0
4
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| 1, 4, 1, 10, 1, 16, 1, 44, 1, 74, 1, 46, 1, 204, 1, 714, 1, 702, 1, 908, 1, 404, 1, 7754, 1, 1136, 1, 9886, 1, 8154, 1, 23578, 1, 65096, 1, 404762, 1, 23992, 1, 3514774, 1, 110124, 1, 4802160, 1, 6490450, 1, 180832, 1, 115972, 1, 770304, 1, 62665998
(list; graph; listen)
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OFFSET
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4,2
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COMMENT
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For n=1,2 a(1)=2, a(2)=1; for n=3 it is not a quadratic surd.
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EXAMPLE
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For n=7 and n=8 the periods after the transient are as follows: cfrac(sqrt(2^7+1),'periodic','quotients'); gives [[11], [2, 1, 3, 1, 6, 1, 3, 1, 2, 22]] cfrac(sqrt(2^8+1),'periodic','quotients'); gives [[16], [32]]
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MAPLE
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with(numtheory): [seq(nops(cfrac(sqrt(2^k+1), 'periodic', 'quotients')[2]), k=4..28)];
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CROSSREFS
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Cf. A059866, A061682.
Adjacent sequences: A059923 A059924 A059925 this_sequence A059927 A059928 A059929
Sequence in context: A028941 A065045 A064947 this_sequence A138775 A121529 A006370
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KEYWORD
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nonn,nice
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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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Two more terms from David W. Wilson (davidwwilson(AT)comcast.net), Jun 18 2001
Corrected and extended by Naohiro Nomoto (n_nomoto(AT)yabumi.com), Nov 09 2001
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