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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 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.)