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.

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

1,9

Comments

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.

Links

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

Example

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

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[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

Crossrefs

Cf. A077762, A077763.

Sequence in context: A065608 A184396 A329718 * A366621 A110794 A117295

Adjacent sequences: A077761 A077762 A077763 * A077765 A077766 A077767

Keyword

nonn

Author

T. D. Noe, Nov 15 2002

Extensions

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

Status

approved