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A214032 Places n where A214030(n) = n-2.

%I A214032 #16 Jul 30 2012 14:01:27
%S A214032 17,67,109,137,181,191,229,233,239,257,283,307,311,349,353,359,479,
%T A214032 523,547,593,599,617,643,709,719,829,839,657,883,907,911,953,977,1021,
%U A214032 1031,1069,1097,1123,1151,1193,1217,1319,1433,1439,1483
%N A214032 Places n where A214030(n) = n-2.
%C A214032 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 A214032 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).
%o A214032 (PARI)
%o A214032 {b23(n)=local(t,m=1,s=[n]); if (n<2,0,while(1,
%o A214032 if(m%2,s=concat(s,2),s=concat(s,3));
%o A214032 t=contfracpnqn(concat(s,n));
%o A214032 t=contfrac(n*t[1,1]/t[2,1]);
%o A214032 if(t[1]<n^2||t[#t]<n^2,m++,break));m)};
%o A214032 /* To print the sequence A214032(n) to the screen, */
%o A214032 for(i=1,1500,if(b23(i)==i-2,print1(i,", ")));
%Y A214032 Cf. A214030, A214031, A000057, A001177.
%K A214032 nonn
%O A214032 1,1
%A A214032 _Art DuPre_, Jul 12 2012