A077763 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.

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, 4005, 8570, 14544, 126725, 124618, 281566, 323297, 382314, 157132, 1374799, 594736, 7274196, 8865745, 27572536, 34358242, 309696376, 457523710, 2659232903, 1429551708, 8294430525

Offset: 1

Author

T. D. Noe, Nov 15 2002

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Bert Dobbelaere, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A077762, A077764.

Programs

Mathematica

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

Extensions

a(29)-a(45) from Bert Dobbelaere, Sep 08 2019