Search: id:A077762 Results 1-1 of 1 results found. %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, Some Problems of Combinatorial Number Theory Related to Bertrand's Postulate, 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 Search completed in 0.001 seconds