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A214034 The apparition sequence for 2,4 continued fractions.

%I A214034 #11 Jan 15 2025 11:48:18
%S A214034 1,2,3,3,5,7,7,2,3,5,11,13,7,11,15,8,5,8,3,23,5,21,23,19,13,8,7,27,11,
%T A214034 31,31,5,17,7,11,37,17,41,7,20,23,20,11,11,21,45,47,7,19,8,27,51,17,
%U A214034 11,7,8,27,14,11,61,31,23,63,27,5,32,35,65,7,69,23,35,37,59,35,23,41,79,15
%N A214034 The apparition sequence for 2,4 continued fractions.
%C A214034 See A214030 for an explanation. There seems to be no corresponding linear recurrence.
%o A214034 (PARI)
%o A214034 {a24(n)=local(t,m=1,s=[n]);if(n<2,0,while(1,
%o A214034 if(m%2,s=concat(s,2),s=concat(s,4));
%o A214034 t=contfracpnqn(concat(s,n));
%o A214034 t=contfrac(n*t[1,1]/t[2,1]);
%o A214034 if(t[1]<n^2||t[#t]<n^2,m++,break));m)};
%o A214034 /* To print out the sequence A214034 */
%o A214034 for(i=2,70,print1(a24(i),", "))
%Y A214034 Cf. A214030.
%K A214034 nonn
%O A214034 1,2
%A A214034 _Art DuPre_, Jul 21 2012
%E A214034 More terms from _Michel Marcus_, Jan 15 2025