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Search: id:A077764
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| A077764 |
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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. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,9
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COMMENT
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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.
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EXAMPLE
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a(5)=1 because only one pairing is possible: 4+49=53, 16+81=97
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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[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
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CROSSREFS
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Cf. A077762, A077763.
Adjacent sequences: A077761 A077762 A077763 this_sequence A077765 A077766 A077767
Sequence in context: A005884 A079890 A065608 this_sequence A110794 A117295 A093820
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KEYWORD
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hard,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Nov 15 2002
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