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
Examples
a(3) = 1, the arrangement is 1,3,6,2,4,5.
References
- R. K. Guy, Unsolved Problems in Number Theory, section C1.
Crossrefs
Cf. A051252.
Programs
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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
Formula
Extensions
a(8)-a(15) from Max Alekseyev, Aug 19 2013
Comments