A077762 -id:A077762 - cp's OEIS frontend

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

T. D. Noe, Nov 15 2002

nonn

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.

			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.

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

Cf. A077762, 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[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

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

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.

Original entry on oeis.org

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, 286, 306, 1312, 1940, 23546, 23886, 23886, 68285, 728501, 241424, 555302, 630441, 4175810, 7996830, 87591010, 101316606, 148078428, 92744140, 298180464, 241949668, 1090944470

Offset: 1

T. D. Noe, Nov 15 2002

nonn

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.

			a(5)=1 because only one pairing is possible: 4+49=53, 16+81=97.

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

Cf. A077762, A077763.

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

a(29)-a(46) from Bert Dobbelaere, Sep 08 2019

cp's OEIS Frontend

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.

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