%I A077762
%S A077762 1,1,0,1,2,0,1,1,4,8,0,8,42,28,140,616,836,180,1416,2542,10960,96048,
%T A077762 242204,367587,923949,1145430,2622420,19081728
%N A077762 Number of ways of pairing the squares of the numbers 1 to n with the 
               squares of the numbers n+1 to 2n such that each pair sums to a prime. 
               Because an odd square must always be added to an even square to obtain 
               a prime, this sequence is the product of A077763 and A077764.
%C A077762 Apparently, for n>11, there seems always to be a pairing possible. Note 
               that all primes have the 4k+1 form. By the 4k+1 theorem, such a prime 
               has a unique representation as the sum of two squares.
%H A077762 L. E. Greenfield and S. J. Greenfield, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">Some Problems of Combinatorial Number Theory 
               Related to Bertrand's Postulate</a>, J. Integer Sequences, 1998, 
               #98.1.2.
%F A077762 a(n)=permanent(m), where the n-by-n matrix m is defined m(i,j) = 1 or 
               0, depending on whether i^2+(j+n)^2 is prime or composite, respectively. 
               - T. D. Noe (noe(AT)sspectra.com), Feb 10 2007
%e A077762 a(5) = 2 because there are two ways: (1,4,9,16,25)+(36,49,100,81,64)=(37,
               53,109,97,89) and (1,4,9,16,25)+(100,49,64,81,36)=(101,53,73,97,61).
%t A077762 lst1*lst2 (* which are defined in A077763 and A077764 *)
%Y A077762 Cf. A000348, A070897, A077763, A077764.
%Y A077762 Sequence in context: A144740 A049501 A102564 this_sequence A085496 A101661 
               A079644
%Y A077762 Adjacent sequences: A077759 A077760 A077761 this_sequence A077763 A077764 
               A077765
%K A077762 hard,nonn
%O A077762 1,5
%A A077762 T. D. Noe (noe(AT)sspectra.com), Nov 15 2002