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A257529 Prime numbers that have a pentagonal Voronoi cell in the Voronoi diagram of the Ulam prime spiral.

%I A257529 #18 Dec 16 2017 18:00:58
%S A257529 2,3,11,13,17,19,29,37,53,83,97,101,103,107,109,113,137,149,151,163,
%T A257529 191,197,211,223,227,241,257,271,281,293,307,337,347,373,401,419,431,
%U A257529 433,461,521,523,541,563,569,571,577,593,619,653,659,673
%N A257529 Prime numbers that have a pentagonal Voronoi cell in the Voronoi diagram of the Ulam prime spiral.
%H A257529 Vardan Semerjyan, <a href="http://smallsats.org/2014/01/03/voronoi-diagram-of-prime-spiral/">Voronoi diagram of prime spiral</a>
%o A257529 (MATLAB)
%o A257529 sz  = 201; % Size of the N x N square matrix
%o A257529 mat = spiral(sz); % MATLAB Function
%o A257529 k = 1;
%o A257529 for i =1:sz
%o A257529     for j=1:sz
%o A257529         if isprime(mat(i,j)) % Check if the number is prime
%o A257529             % saving indices of primes
%o A257529             y(k) = i; x(k) = j;
%o A257529             k = k+1;
%o A257529         end
%o A257529     end
%o A257529 end
%o A257529 xy = [x',y'];
%o A257529 [v,c] = voronoin(xy); %  Returns Voronoi vertices V and
%o A257529 % the Voronoi cells C
%o A257529 k = 1;
%o A257529 for i = 1:length(c)
%o A257529   szv = size(v(c{i},1));
%o A257529   polyN(i) = szv(1);
%o A257529   if polyN(i) == 5
%o A257529         A(k) = mat(y(i),x(i));
%o A257529         k = k+1;
%o A257529       end
%o A257529 end
%o A257529 % Print terms
%o A257529 A = sort(A);
%o A257529 fprintf('A = ');
%o A257529 fprintf('%i, ',A);
%o A257529 % Note that the last terms might not be correct.
%o A257529 % They correspond to the points on the outer edges of the spiral which might be altered when considering a larger spiral.
%o A257529 % Use larger spiral to get more terms
%Y A257529 Cf. A257527, A257528, A000040, A077800.
%K A257529 nonn
%O A257529 1,1
%A A257529 _Vardan Semerjyan_, Apr 28 2015