Search: id:A146334
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%I A146334
%S A146334 43,67,116,129,134,161,162,184,218,242,243,246,270,274,297,301,314,338,
%T A146334 339,345,354,356,407,411,451,452,459,465,475,498,515,517,532,534,561,
%U A146334 563,590,591,595,597,603,611,638,648,657,665,669,671,690,705,715
%N A146334 Numbers k such that continued fraction of (1+Sqrt[k])/2 has period 10
%C A146334 For primes in this sequence see A146355.
%e A146334 a(1) = 43 because continued fraction of (1+Sqrt[43])/2 = 3, 1, 3, 1, 
               1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 
               12, 1, 1, 3, 1, ...
%e A146334 has period (1, 3, 1, 1, 12, 1, 1, 3, 1, 5) length 10
%p A146334 A146326 := proc(n) if not issqr(n) then numtheory[cfrac]( (1+sqrt(n))/
               2, 'periodic','quotients') ; nops(%[2]) ; else 0 ; fi; end: isA146334 
               := proc(n) RETURN(A146326(n) = 10) ; end: for n from 2 to 715 do 
               if isA146334(n) then printf("%d,",n) ; fi; od: [From R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Sep 06 2009]
%t A146334 s = 10; aa = {}; Do[k = ContinuedFraction[(1 + Sqrt[n])/2, 1000]; If[Length[k] 
               < 190, AppendTo[aa, 0], m = 1; While[k[[s ]] != k[[s + m]] || k[[s 
               + m]] != k[[s + 2 m]] || k[[s + 2 m]] != k[[s + 3 m]] || k[[s + 3 
               m]] != k[[s + 4 m]], m++ ]; s = s + 1; While[k[[s ]] != k[[s + m]] 
               || k[[s + m]] != k[[s + 2 m]] || k[[s + 2 m]] != k[[s + 3 m]] || 
               k[[s + 3 m]] != k[[s + 4 m]], m++ ]; s = s + 1; While[k[[s ]] != 
               k[[s + m]] || k[[s + m]] != k[[s + 2 m]] || k[[s + 2 m]] != k[[s 
               + 3 m]] || k[[s + 3 m]] != k[[s + 4 m]], m++ ]; AppendTo[aa, m]], 
               {n, 1, 500}]; bb = {}; Do[If[aa[[n]] == 10, AppendTo[bb, n]], {n, 
               1, Length[aa]}]; bb (*Artur Jasinski*)
%Y A146334 A000290, A078370, A146326-A146345, A146348-A146360.
%Y A146334 Sequence in context: A020349 A050959 A139917 this_sequence A039385 A043208 
               A043988
%Y A146334 Adjacent sequences: A146331 A146332 A146333 this_sequence A146335 A146336 
               A146337
%K A146334 nonn
%O A146334 1,1
%A A146334 Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008
%E A146334 284 removed by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 06 2009

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