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A214031 Fixed points of A214030. 4


%S 13,19,23,37,41,47,89,139,157,211,277,281,331,373,379,397,499,503,521,

%T 571,613,619,641,647,691,733,739,743,757,761,811,853,859,863,877,983,

%U 997,1051,1093,1103,1117,1171,1213,1223,1237,1289,1297,1409,1453,1459,1481,1487

%N Fixed points of A214030.

%C 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 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 {n: A214030(n)=n}.

%o (PARI)

%o {b23(n)=local(t,m=1,s=[n]); if (n<2,0,while(1,

%o if(m%2,s=concat(s,2),s=concat(s,3));

%o t=contfracpnqn(concat(s,n));

%o t=contfrac(n*t[1,1]/t[2,1]);

%o if(t[1]<n^2||t[#t]<n^2,m++,break));m)};

%o To print the sequence A214031(n) to the screen,

%o for(i=1,500,if(b23(i)==i,print1(i,", ")));

%Y Cf. A000057, A001177, A214030.

%K nonn

%O 1,1

%A _Art DuPre_, Jul 12 2012

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Last modified January 18 16:27 EST 2020. Contains 331011 sequences. (Running on oeis4.)