a(5)=3 since A077722(5)=32833, which has an octal form of 100101, which has 3 ones.

MAPLE

s := 0:for n from 1 to 7000 do b := convert(n, base, 2):q := sum(b[i]*8^(i-1), i=1..nops(b)): if(isprime(q)) then s := s+1:a[s] := sum(b[i], i=1..nops(b)):fi:od:seq(a[k], k=1..s);