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%I #11 Sep 08 2019 03:13:32
%S 1,1,0,1,2,0,1,1,2,2,0,1,7,2,10,14,38,6,118,62,80,144,604,711,6201,
%T 4005,8570,14544,126725,124618,281566,323297,382314,157132,1374799,
%U 594736,7274196,8865745,27572536,34358242,309696376,457523710,2659232903,1429551708,8294430525
%N Number of ways of pairing the odd squares of the numbers 1 to n with the even squares of the numbers n+1 to 2n such that each pair sums to a prime.
%C 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 A077764 gives A077762.
%H Bert Dobbelaere, <a href="/A077763/b077763.txt">Table of n, a(n) for n = 1..50</a>
%e a(5)=2 because two pairings are possible: 1+36=37, 9+100=109, 25+64=89 and 1+100=101, 9+64=73, 25+36=61.
%t 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[lst1={1}; n=2, n<=maxN, n++, s=Table[{}, {n}]; For[i=1, 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[1]; AppendTo[lst1, cnt]]; lst1
%Y Cf. A077762, A077764.
%K nonn
%O 1,5
%A _T. D. Noe_, Nov 15 2002
%E a(29)-a(45) from _Bert Dobbelaere_, Sep 08 2019
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