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%I #19 Jul 30 2012 14:06:26
%S 13,17,19,23,37,41,47,67,89,109,137,139,157,181,191,211,229,233,239,
%T 257,277,281,283,307,311,331,349,353,359,373,379,397,479,499,503,521,
%U 523,547,571,593,599,613,617,619,641
%N Places n where A214030(n) = n or A214030(n) = n-2.
%C It always has been one of the great mysteries of mathematics, that the superdiagonal sequence of A001177 consists of prime numbers A000057.
%C Here, regarding A214031 and A214032,there is the further conjecture that these two disjoint sequences are primes and roughly comparable in density. It isn't clear that these two sequences have a density, without appealing to the Riemann Hypothesis, but they are certainly close to one another in growing size.
%C Since these two sequences are disjoint, it is natural to take their union.
%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 a(n) to the screen,
%o for(i=1,500,if(b23(i)==i||b23(i)==i-2,
%o print1(i,", ")));
%Y Cf. A000057, A001177, A214030-A213032.
%K nonn
%O 1,1
%A _Art DuPre_, Jul 12 2012
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