%I A077764
%S A077764 1,1,1,1,1,1,1,1,2,4,4,8,6,14,14,44,22,30,12,41,137,667,401,517,149,
%T A077764 286,306,1312
%N A077764 Number of ways of pairing the even squares of the numbers 1 to n with 
               the odd squares of the numbers n+1 to 2n such that each pair sums 
               to a prime. a(1) is defined to be 1.
%C A077764 It appears that a pairing is always possible. The Mathematica program 
               uses backtracking to find all solutions. The Print statement can 
               be uncommented to print all solutions. The product of this sequence 
               and A077763 gives A077762.
%e A077764 a(5)=1 because only one pairing is possible: 4+49=53, 16+81=97
%t A077764 try[lev_] := Module[{j}, If[lev>n, (*Print[soln]; *) cnt++, For[j=1, 
               j<=Length[s[[lev]]], j++, If[ !MemberQ[soln, s[[lev]][[j]]], soln[[lev]]=s[[lev]][[j]]; 
               try[lev+2]; soln[[lev]]=0]]]]; maxN=28; For[lst2={1}; n=2, n<=maxN, 
               n++, s=Table[{}, {n}]; For[i=2, i<=n, i=i+2, For[j=n+1, j<=2n, j++, 
               If[PrimeQ[i^2+j^2], AppendTo[s[[i]], j]]]]; soln=Table[0, {n}]; cnt=0; 
               try[2]; AppendTo[lst2, cnt]]; lst2
%Y A077764 Cf. A077762, A077763.
%Y A077764 Sequence in context: A005884 A079890 A065608 this_sequence A110794 A117295 
               A093820
%Y A077764 Adjacent sequences: A077761 A077762 A077763 this_sequence A077765 A077766 
               A077767
%K A077764 hard,nonn
%O A077764 1,9
%A A077764 T. D. Noe (noe(AT)sspectra.com), Nov 15 2002