cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A146334 Numbers k such that continued fraction of (1 + sqrt(k))/2 has period 10.

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%I A146334 #15 Mar 31 2020 03:44:26
%S A146334 43,67,116,129,134,161,162,184,218,242,243,246,270,274,297,301,314,
%T A146334 338,339,345,354,356,407,411,451,452,459,465,475,498,515,517,532,534,
%U A146334 561,563,590,591,595,597,603,611,638,648,657,665,669,671,690,705,715
%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.
%H A146334 Amiram Eldar, <a href="/A146334/b146334.txt">Table of n, a(n) for n = 1..10000</a>
%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, ... 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: # _R. J. Mathar_, Sep 06 2009
%t A146334 cf10Q[n_]:=Module[{s=(1+Sqrt[n])/2,x},x=If[IntegerQ[s],1,Length[ ContinuedFraction[ s][[2]]]];x==10]; Select[Range[750],cf10Q] (* _Harvey P. Dale_, Sep 22 2015 *)
%Y A146334 Cf. A000290, A078370, A146326-A146345, A146348-A146360.
%K A146334 nonn
%O A146334 1,1
%A A146334 _Artur Jasinski_, Oct 30 2008
%E A146334 284 removed by _R. J. Mathar_, Sep 06 2009