cp's OEIS Frontend

A072129 Number of distinct ways of arranging the squares {1,4,9,...,(2n)^2} in a circle so that the sum of each two adjacent entries is a prime.

%I A072129 #13 Sep 03 2024 16:12:30
%S A072129 1,0,0,0,6,0,96,272,1408,61622,33736,356606,86520774,192570133,
%T A072129 1560696233
%N A072129 Number of distinct ways of arranging the squares {1,4,9,...,(2n)^2} in a circle so that the sum of each two adjacent entries is a prime.
%e A072129 a(5)=6 because there are 6 essentially different ways: {1, 4, 9, 64, 49, 100, 81, 16, 25, 36}, {1, 4, 49, 64, 9, 100, 81, 16, 25, 36}, {1, 16, 81, 100, 9, 4, 49, 64, 25, 36}, {1, 16, 81, 100, 9, 64, 49, 4, 25, 36}, {1, 16, 81, 100, 49, 4, 9, 64, 25, 36} and {1, 16, 81, 100, 49, 64, 9, 4, 25, 36}
%t A072129 $RecursionLimit=500; try[lev_] := Module[{t, j}, If[lev>2n, (*then make sure the sum of the first and last is prime*) If[PrimeQ[soln[[1]]^2+soln[[2n]]^2]&&soln[[2]]<=soln[[2n]], (*Print[soln]; *) cnt++ ], (*else append another number to the soln list*) t=soln[[lev-1]]; For[j=1, j<=Length[s[[t]]], j++, If[ !MemberQ[soln, s[[t]][[j]]], soln[[lev]]=s[[t]][[j]]; try[lev+1]; soln[[lev]]=0]]]]; For[lst={}; n=1, n<=7, n++, s=Table[{}, {2n}]; For[i=1, i<=2n, i++, For[j=1, j<=2n, j++, If[i!=j&&PrimeQ[i^2+j^2], AppendTo[s[[i]], j]]]]; soln=Table[0, {2n}]; soln[[1]]=1; cnt=0; try[2]; AppendTo[lst, cnt]]; lst
%Y A072129 Cf. A051252, A073451.
%K A072129 nonn,more
%O A072129 1,5
%A A072129 _Santi Spadaro_, Jun 25 2002
%E A072129 Corrected and extended by _T. D. Noe_, Jul 03 2002
%E A072129 a(13) corrected and a(14)-a(15) from _Sean A. Irvine_, Sep 03 2024