

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.


2



0, 0, 1, 44, 912, 61952, 8160260, 888954284, 180955852060, 50317255621843, 12251146829850324, 4243527581615332664, 1602629887788636447221, 622433536382831426225696, 344515231090957672408413959
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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*n1)
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*n1)
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



