cp's OEIS Frontend

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.

%I A077764 #10 Sep 08 2019 03:14:14
%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 286,306,1312,1940,23546,23886,23886,68285,728501,241424,555302,
%U A077764 630441,4175810,7996830,87591010,101316606,148078428,92744140,298180464,241949668,1090944470
%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.
%H A077764 Bert Dobbelaere, <a href="/A077764/b077764.txt">Table of n, a(n) for n = 1..50</a>
%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.
%K A077764 nonn
%O A077764 1,9
%A A077764 _T. D. Noe_, Nov 15 2002
%E A077764 a(29)-a(46) from _Bert Dobbelaere_, Sep 08 2019