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 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. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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; AppendTo[lst2, cnt]]; lst2 CROSSREFS Cf. A077762, A077763. Sequence in context: A065608 A184396 A329718 * A110794 A117295 A235999 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

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Last modified January 16 06:48 EST 2021. Contains 340204 sequences. (Running on oeis4.)