Cheers,

2 PRE-NUMBERED NEW SEQUENCES A095749 & A095759.
The rows are a bit full, as I explicitly added
three and four more terms to the end of %U-lines
(after my auto-formatting Scheme-program had
cut the lines to appropriate < 80 chars. length),
so as to get nice triangular lengths 55 and 91
for these.
The rows and columns (i.e. the sequences) come
a bit later.


%I A095749
%S A095749 3,5,2,7,11,43,17,13,53,151,31,19,71,179,599,73,23,79,233,683,2111,107,
%T A095749 29,83,241,739,2143,8543,127,37,101,271,797,2503,9103,33023,257,41,109,
%U A095749 311,853,2731,9623,33151,131839,313,47,113,331,937,3011,10427,33599,135647,531071
%N A095749 Square array A(row>=1, col>=1) by antidiagonals: A(r,c) contains c:th prime p for which A037888(p)=(row-1).
%e A095749 a(1) = A(1,1) = 3 (11 in binary) as it is the first prime whose binary expansion is palindromic. a(2) = A(1,2) = 5 (101 in binary) as it is the second prime whose binexp is palindromic. a(3) = A(2,1) = 2 (10 in binary) as it is the first prime whose binexp needs a flip of just one bit to become palindrome. a(4) = A(1,3) = 7 (111 in binary) as it is the third prime whose binexp is palindromic. a(5) = A(2,2) = 11 (1011 in binary) as it is the second prime whose binexp needs a flip of just one bit to become palindrome.
%Y A095749 Row 1: A016041, 2: A095743, 3: A095744, 4: A095745, 5: A095746. Cf. also A095759. A095747-A095748. Permutation of primes (A000040).
%K A095749 nonn
%O A095749 1,1
%A A095749 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jun 12 2004

%I A095759
%S A095759 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 A095759 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 A095759 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 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.
%e A095759 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 A095759 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 A095759 nonn
%O A095759 0,2
%A A095759 Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jun 12 2004