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A214031 Fixed points of A214030.

%I A214031 #28 Jan 15 2025 11:24:26
%S A214031 13,19,23,37,41,47,89,139,157,211,277,281,331,373,379,397,499,503,521,
%T A214031 571,613,619,641,647,691,733,739,743,757,761,811,853,859,863,877,983,
%U A214031 997,1051,1093,1103,1117,1171,1213,1223,1237,1289,1297,1409,1453,1459,1481,1487
%N A214031 Fixed points of A214030.
%C A214031 This sequence is to A214030 as A000057 is to A001177. It would be nice to have an interpretation of this sequence akin to the interpretation of A000057 as the set of primes which divide all Fibonacci sequences, having arbitrary initial values for a(1),a(2). The linearly recursive sequence which seems to be associated to this is 3*f(n) = 6*f(n-1) + 2*f(n-2), but this does not have integral values.
%C A214031 If we use the sequence 3,2,3,2,3,2,... instead of 2,3,2,3,... we end up with the same sequence a(n).
%F A214031 {n: A214030(n)=n}.
%o A214031 (PARI)
%o A214031 {b23(n)=local(t,m=1,s=[n]); if (n<2,0,while(1,
%o A214031 if(m%2,s=concat(s,2),s=concat(s,3));
%o A214031 t=contfracpnqn(concat(s,n));
%o A214031 t=contfrac(n*t[1,1]/t[2,1]);
%o A214031 if(t[1]<n^2||t[#t]<n^2,m++,break));m)};
%o A214031 \\ To print the sequence A214031(n) to the screen,
%o A214031 for(i=1,500,if(b23(i)==i,print1(i,", ")));
%Y A214031 Cf. A000057, A001177, A214030.
%K A214031 nonn
%O A214031 1,1
%A A214031 _Art DuPre_, Jul 12 2012