cp's OEIS Frontend

A214029 The union of the disjoint prime sequences A000057 and A106535.

%I A214029 #19 Jul 13 2012 14:45:07
%S A214029 2,3,7,11,19,23,31,43,59,67,71,79,83,103,127,131,163,167,179,191,223,
%T A214029 227,239,251,271,283,311,359,367,379,383,419,431,439,443,463,467,479,
%U A214029 487,491,499,503,523,547,571,587,599,607,631,643,647,659,683,719,727
%N A214029 The union of the disjoint prime sequences A000057 and A106535.
%C A214029 Just as A000057 can be generated by looking at the subscripts of the sequence A001177 which are one less than their values, A106535 can be generated by looking at the subscripts of the sequence A001177 which are one greater than their values.
%C A214029 It is a surprising fact that these two sequences A000057 and A106535 are disjoint. The also have approximately the same density, if these densities exist.
%C A214029 It would be interesting to be able to interpret the relation of this prime sequence to the entire set of Fibonacci sequences, i.e., those sequences satisfying f(n+2) = f(n+1) + f(n) with various initial conditions.
%o A214029 (PARI) {a(n,p) = local(t, m=1,s=[n]); if( n<2, 0, while( 1,
%o A214029    s=concat(s,p);
%o A214029 t=contfracpnqn(concat(s,n));
%o A214029    t = contfrac(n*t[1,1]/t[2,1]);
%o A214029    if(t[1]<n^2 || t[#t]<n^2, m++, break));
%o A214029 m)};
%o A214029 {p(m,n,p)=for(k=m,n,if(k-2==a(k,p)||k==a(k,p),print1(k,”, “)));}
%o A214029 p(1,800,1);
%Y A214029 Cf. A000057, A001177, A106535.
%K A214029 nonn
%O A214029 1,1
%A A214029 _Art DuPre_, Jul 09 2012