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A077763
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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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2
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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
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OFFSET
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1,5
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..28.
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EXAMPLE
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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
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MATHEMATICA
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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
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CROSSREFS
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Cf. A077762, A077764.
Sequence in context: A026931 A127506 A007968 * A030218 A127440 A118198
Adjacent sequences: A077760 A077761 A077762 * A077764 A077765 A077766
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KEYWORD
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hard,nonn
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AUTHOR
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T. D. Noe, Nov 15 2002
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STATUS
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approved
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