Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 Jul 17 2014 22:34:31
%S 0,1,1,2,0,2,5,11,6,28,39,57,96,163,324,486,967,1493,2915,5083,9343,
%T 16836,31877,55587,105785,189879,357614,664588,1257356,2254304,
%U 4303412,8113964,15259583,28364673
%N Number of primes whose binary representation has length n and which translates ('inter-base translation') to ternary as a prime.
%e The only binary 5-digit (-bit) primes are decimal 17, 19, 23, 29 and 31; and reading the binary representations of these as base-3 representations instead produces numbers whose decimal representations are 82, 85, 94, 118 and 121. None of these 5 numbers are prime, so a(5)=0.
%o (PARI)
%o {
%o i=1;while(1,
%o z=0;forprime(p=2^(i-1),2^i-1,
%o b=binary(p);u=0;for(j=1,i,
%o if(b[j],u+=3^(i-j)));if(isprime(u),z++));
%o print1(z", ");i++)
%o }
%Y Cf. A235266.
%K nonn,base
%O 1,4
%A _James G. Merickel_, May 31 2014