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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 4 04:22 EST 2020. Contains 338921 sequences. (Running on oeis4.)