%I A086386
%S A086386 5,19,71,3691,191861,26947261171
%N A086386 Numerators of the rational convergents to sqrt(3) if both numerators 
               and denominators are primes.
%C A086386 These numbers are rare.
%C A086386 General recurrence is a(n)=(a(1)-1)*a(n-1)-a(n-2), a(1)>=4, lim n->infinity 
               a(n)= x*(k*x+1)^n, k =(a(1)-3), x=(1+sqrt((a(1)+1)/(a(1)-3)))/2. 
               Examples in OEIS: a(1)=4 gives A002878, primes in it A121534. a(1)=5 
               gives A001834, primes in it A086386. a(1)=6 gives A030221, primes 
               in it not in OEIS {29,139,3191,...}. a(1)=7 gives A002315, primes 
               in it A088165. a(1)=8 gives A033890, primes in it not in OEIS (does 
               there exist any ?). a(1)=9 gives A057080, primes in it not in OEIS 
               {71,34649,16908641,...}. a(1)=10 gives A057081, primes in it not 
               in OEIS {389806471,192097408520951,...}. [From Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), 
               Sep 02 2008]
%o A086386 (PARI) cfracnum(m,f) = { cfr = vector(10000); x=f; for(n=0,m, i=floor(x); 
               x=1/(x-i); cfr[n+1] = i; ); for(m1=0,m, r=cfr[m1+1]; forstep(n=m1,
               1,-1, r = 1/r; r+=cfr[n]; ); numer=numerator(r); denom=denominator(r); 
               if(isprime(numer) & isprime(denom),print1(numer",")); ) }
%Y A086386 Sequence in context: A149760 A149761 A149762 this_sequence A047155 A034548 
               A129166
%Y A086386 Adjacent sequences: A086383 A086384 A086385 this_sequence A086387 A086388 
               A086389
%K A086386 nonn
%O A086386 1,1
%A A086386 Cino Hilliard (hillcino368(AT)gmail.com), Sep 06 2003