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

1,5

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.

Links

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

Example

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.

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

Crossrefs

Cf. A077762, A077764.

Sequence in context: A353433 A007968 A236532 * A030218 A281388 A127440

Adjacent sequences: A077760 A077761 A077762 * A077764 A077765 A077766

Keyword

nonn

Author

T. D. Noe, Nov 15 2002

Extensions

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

Status

approved