Search: id:A059926
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%I A059926
%S A059926 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,
%T A059926 1136,1,9886,1,8154,1,23578,1,65096,1,404762,1,23992,1,3514774,1,
%U A059926 110124,1,4802160,1,6490450,1,180832,1,115972,1,770304,1,62665998
%N A059926 Quotient cycle length in continued fraction expansion of sqrt(2^n+1).
%C A059926 For n=1,2 a(1)=2, a(2)=1; for n=3 it is not a quadratic surd.
%e A059926 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]]
%p A059926 with(numtheory): [seq(nops(cfrac(sqrt(2^k+1),'periodic','quotients')[2]),
               k=4..28)];
%Y A059926 Cf. A059866, A061682.
%Y A059926 Sequence in context: A028941 A065045 A064947 this_sequence A138775 A121529 
               A006370
%Y A059926 Adjacent sequences: A059923 A059924 A059925 this_sequence A059927 A059928 
               A059929
%K A059926 nonn,nice
%O A059926 4,2
%A A059926 Labos E. (labos(AT)ana.sote.hu), Mar 01 2001
%E A059926 Two more terms from David W. Wilson (davidwwilson(AT)comcast.net), Jun 
               18 2001
%E A059926 Corrected and extended by Naohiro Nomoto (n_nomoto(AT)yabumi.com), Nov 
               09 2001

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