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A257749 Prime numbers that have a dodecagonal (12 sides) Voronoi cell in the Voronoi diagram of the Ulam prime spiral.

%I A257749 #9 Dec 16 2017 18:03:23
%S A257749 61673,635939,706117,720743,1483439,1742501,1766701,1847603,2097959,
%T A257749 2163461,2365289,2429411,3420101,3490703,3657361,3920843,3973829,
%U A257749 4758973,4920887,4989779,5273753,6167687,6223247,6573559,6655409,6694333,6791881,7095503,7102349,7338293,7644541
%N A257749 Prime numbers that have a dodecagonal (12 sides) Voronoi cell in the Voronoi diagram of the Ulam prime spiral.
%H A257749 Vardan Semerjyan, <a href="http://smallsats.org/2014/01/03/voronoi-diagram-of-prime-spiral/">Voronoi diagram of prime spiral</a>
%o A257749 (MATLAB)
%o A257749 sz  = 3001; % Size of the N x N square matrix
%o A257749 mat = spiral(sz); % MATLAB Function
%o A257749 k = 1;
%o A257749 for i =1:sz
%o A257749     for j=1:sz
%o A257749         if isprime(mat(i,j)) % Check if the number is prime
%o A257749             % saving indices of primes
%o A257749             y(k) = i; x(k) = j;
%o A257749             k = k+1;
%o A257749         end
%o A257749     end
%o A257749 end
%o A257749 xy = [x',y'];
%o A257749 [v,c] = voronoin(xy); %  Returns Voronoi vertices V and
%o A257749 % the Voronoi cells C
%o A257749 k = 1;
%o A257749 for i = 1:length(c)
%o A257749   szv = size(v(c{i},1));
%o A257749   polyN(i) = szv(1);
%o A257749   if polyN(i) == 12
%o A257749         A(k) = mat(y(i),x(i));
%o A257749         k = k+1;
%o A257749       end
%o A257749 end
%o A257749 % Print terms
%o A257749 A = sort(A);
%o A257749 fprintf('A = ');
%o A257749 fprintf('%i, ',A);
%o A257749 % When running the code be aware that the last terms you get might not be correct.
%o A257749 % They correspond to the points on the outer edges of the spiral which might be
%o A257749 % altered when considering a larger spiral.
%o A257749 % Use larger spiral to get more terms
%Y A257749 Cf. A257527, A257528, A000040.
%K A257749 nonn
%O A257749 1,1
%A A257749 _Vardan Semerjyan_, May 07 2015