A095759 Triangle T(row>=0, 0<= pos <=row) by rows: T(r,p) contains number of odd primes p in range [2^(r+1),2^(r+2)] for which A037888(p)=pos.
1, 2, 0, 0, 2, 0, 2, 3, 0, 0, 0, 5, 2, 0, 0, 3, 4, 6, 0, 0, 0, 0, 15, 4, 4, 0, 0, 0, 3, 18, 15, 7, 0, 0, 0, 0, 0, 32, 20, 16, 7, 0, 0, 0, 0, 7, 33, 63, 24, 10, 0, 0, 0, 0, 0, 0, 63, 62, 88, 33, 9, 0, 0, 0, 0, 0, 12, 81, 135, 154, 56, 26, 0, 0, 0, 0, 0, 0, 0, 119, 150, 314, 197, 72, 20, 0, 0, 0, 0, 0, 0
Offset: 0
Examples
a(0) = T(0,0) = 1 as there is one prime 3 (11 in binary) in range ]2^1,2^2[ whose binary expansion is palindromic. a(1) = T(1,0) = 2 as there are two primes, 5 and 7 (101 and 111 in binary) in range ]2^2,2^3[ whose binary expansions are palindromic. a(2) = T(1,1) = 0, as there are no other primes in that range. a(3) = T(2,0) = 0, as there are no palindromic primes in range ]2^3,2^4[, but a(4) = T(2,1) = 2 as in the same range there are two primes 11 and 13 (1011 and 1101 in binary), whose binary expansion needs a flip of just one bit to become palindrome.
Crossrefs
Row sums: A036378. Bisection of the leftmost diagonal: A095741. Next diagonals: A095753, A095754, A095755, A095756. Central diagonal (column): A095760. The rightmost nonzero terms from each row: A095757 (i.e. central diagonal and next-to-central diagonal interleaved). The penultimate nonzero terms from each row: A095758. Cf. also A095749, A048700-A048704, A095742.