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.

0, 0, 1, 44, 912, 61952, 8160260, 888954284, 180955852060, 50317255621843, 12251146829850324, 4243527581615332664, 1602629887788636447221, 622433536382831426225696, 344515231090957672408413959

Offset

1,4

Comments

One of the obvious analogs of sequence A051252, which has the sums being prime. Presumably it is an open problem as to whether a(n) > 0 always for this problem as well.

The Guy reference deals with each adjacent pair summing to a prime. - T. D. Noe, Jun 08 2011

References

R. K. Guy, Unsolved Problems in Number Theory, section C1.

Links

Table of n, a(n) for n=1..15.

Formula

Bisection of A182540: a(n) = A182540(2*n). - Max Alekseyev, Aug 18 2013

Example

a(3) = 1, the arrangement is 1,3,6,2,4,5.

Prog

(MATLAB)
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
toc

Crossrefs

Cf. A051252.

Sequence in context: A183750 A133349 A010838 * A299466 A010960 A035717

Adjacent sequences: A191371 A191372 A191373 * A191375 A191376 A191377

Keyword

nonn,more

Author

Bennett Gardiner, Jun 01 2011

Extensions

a(8)-a(15) from Max Alekseyev, Aug 19 2013

Status

approved