%I A101415
%S A101415 2,3,7,13,19,29,31,41,43,59,67,71,73,89
%N A101415 Amenable primes of order 3. Primes p such that the numerator and denominator 
               of the continued fraction rational approximation of the sqrt(p) are 
               both prime and the numerator is less than 10^3 digits in length.
%C A101415 Amenable primes of order k are also amenable primes of order k+1.
%e A101415 13 is in the list because 7/2 is rational convergent of sqrt(13) and 
               the length of 7 is < 10^3 and 7 and 2 are primes. 11/3 is the only 
               other convergent for the sqrt(13) that has a numerator < 10^3 digits.
%o A101415 (PARI) cfracnumdenomprime(m,f) = { default(realprecision,3000); cf = 
               vector(m+10); x=f; for(n=0,m, i=floor(x); x=1/(x-i); cf[n+1] = i; 
               ); for(m1=0,m, r=cf[m1+1]; forstep(n=m1,1,-1, r = 1/r; r+=cf[n]; 
               ); numer=numerator(r); denom=denominator(r); if(ispseudoprime(numer)&&ispseudoprime(denom),
               print1(numer",");numer2=numer;denom2=denom); if(length(Str(numer))>
               999,break); ) }
%Y A101415 Sequence in context: A100764 A076974 A051484 this_sequence A045331 A053613 
               A013645
%Y A101415 Adjacent sequences: A101412 A101413 A101414 this_sequence A101416 A101417 
               A101418
%K A101415 frac,nonn
%O A101415 1,1
%A A101415 Cino Hilliard (hillcino368(AT)gmail.com), Jan 16 2005