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A257747 Prime numbers that have an octagonal (8 sides) Voronoi cell in the Voronoi diagram of the Ulam prime spiral.

%I A257747 #9 Dec 16 2017 18:02:22
%S A257747 67,491,613,1013,1117,1201,1249,1301,1373,1543,1753,1907,2017,2339,
%T A257747 2411,2657,2671,2879,3023,3037,3181,3677,3727,3733,4139,4409,4549,
%U A257747 4861,5303,5381,5399,5857,5897,6301,6373,6737,7433,7499,7577,7583
%N A257747 Prime numbers that have an octagonal (8 sides) Voronoi cell in the Voronoi diagram of the Ulam prime spiral.
%H A257747 Vardan Semerjyan, <a href="http://smallsats.org/2014/01/03/voronoi-diagram-of-prime-spiral/">Voronoi diagram of prime spiral</a>
%o A257747 (MATLAB)
%o A257747 sz  = 201; % Size of the N x N square matrix
%o A257747 mat = spiral(sz); % MATLAB Function
%o A257747 k = 1;
%o A257747 for i =1:sz
%o A257747     for j=1:sz
%o A257747         if isprime(mat(i,j)) % Check if the number is prime
%o A257747             % saving indices of primes
%o A257747             y(k) = i; x(k) = j;
%o A257747             k = k+1;
%o A257747         end
%o A257747     end
%o A257747 end
%o A257747 xy = [x',y'];
%o A257747 [v,c] = voronoin(xy); %  Returns Voronoi vertices V and
%o A257747 % the Voronoi cells C
%o A257747 k = 1;
%o A257747 for i = 1:length(c)
%o A257747   szv = size(v(c{i},1));
%o A257747   polyN(i) = szv(1);
%o A257747   if polyN(i) == 8
%o A257747         A(k) = mat(y(i),x(i));
%o A257747         k = k+1;
%o A257747       end
%o A257747 end
%o A257747 % Print terms
%o A257747 A = sort(A);
%o A257747 fprintf('A = ');
%o A257747 fprintf('%i, ',A);
%o A257747 % When running the code be aware that the last terms you get might not be correct.
%o A257747 % They correspond to the points on the outer edges of the spiral which might be
%o A257747 % altered when considering a larger spiral.
%o A257747 % Use larger spiral to get more terms
%Y A257747 Cf. A257527, A257528, A000040.
%K A257747 nonn
%O A257747 1,1
%A A257747 _Vardan Semerjyan_, May 07 2015