Bennett Gardiner has authored 2 sequences.
A191798
Number of essentially different ways of arranging numbers 1 through 2*n around a circle so that the sums of each pair of adjacent numbers are neither all prime nor all composite.
Original entry on oeis.org
0, 2, 58, 2474, 180480, 19895936, 3105348340, 652948189204, 177662757810868, 60772232945639507, 25533219938917963508, 12921764841857675170314, 7754002391777621430686566
Offset: 1
a(2) = 2 since the arrangements 1,3,2,4 and 1,3,4,2 both satisfy the condition.
A191374
Number of ways (up to rotations and reflections) of arranging numbers 1 through 2n around a circle such that the sum of each pair of adjacent numbers is composite.
Original entry on oeis.org
0, 0, 1, 44, 912, 61952, 8160260, 888954284, 180955852060, 50317255621843, 12251146829850324, 4243527581615332664, 1602629887788636447221, 622433536382831426225696, 344515231090957672408413959
Offset: 1
a(3) = 1, the arrangement is 1,3,6,2,4,5.
- R. K. Guy, Unsolved Problems in Number Theory, section C1.
-
function D=primecirc(n)
tic
a = 2:2*n;
A=perms(a);
for i =1:factorial(2*n-1)
B(i,:)=[1 A(i,:)];
end
for k=1:size(B,2)-1
F(:,k) = B(:,k)+B(:,k+1);
end
if k>1
F(:,k+1)=B(:,end)+B(:,1);
end
l=1;
for i=1:factorial(2*n-1)
if ~isprime(F(i,:)) == ones(1,length(B(1,:)))
C(l,:)=B(i,:);
l=l+1;
end
end
if ~exist('C')
D=0;
return
end
if size(C,1)==1
D=1;
else
D=size(C,1)/2;
end
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