cp's OEIS Frontend

A059926 Length of period of the continued fraction expansion of sqrt(2^n+1).

%I A059926 #25 Oct 04 2019 13:09:45
%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 110124,1,4802160,1,6490450,1,180832,1,115972,1,770304,1,62665998,1,133093360,1,1019300318,1,60079334
%N A059926 Length of period of the 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.
%H A059926 Chai Wah Wu, <a href="/A059926/b059926.txt">Table of n, a(n) for n = 4..84</a>
%F A059926 a(n) =  A003285(A000051(n)). - _Michel Marcus_, Sep 27 2019
%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)];
%t A059926 Table[Length[ContinuedFraction[Sqrt[2^n+1]][[2]]],{n,4,60}] (* _Harvey P. Dale_, Feb 05 2012 *)
%Y A059926 Cf. A000051, A003285, A059866, A061682.
%K A059926 nonn,nice
%O A059926 4,2
%A A059926 _Labos Elemer_, Mar 01 2001
%E A059926 Two more terms from _David W. Wilson_, Jun 18 2001
%E A059926 Corrected and extended by _Naohiro Nomoto_, Nov 09 2001
%E A059926 a(58)-a(63) from _Daniel Suteu_, Jan 25 2019