A095759 - OEIS

%I #2 Mar 31 2012 14:02:20

%S 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,

%T 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,

%U 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

%N 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.

%e 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.

%Y 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.

%K nonn,tabl

%O 0,2

%A _Antti Karttunen_, Jun 12 2004