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A257748 Prime numbers that have a decagonal (10 sides) Voronoi cell in the Voronoi diagram of the Ulam prime spiral.

%I A257748 #9 Dec 16 2017 18:02:59
%S A257748 8741,9533,11087,14629,17077,26029,29723,33247,38723,40177,43991,
%T A257748 45677,56369,57709,58027,68749,77479,81727,88117,90173,93053,110933,
%U A257748 112297,112901,114859,117773,127219,129841,131771,146161,156719,159293,169369
%N A257748 Prime numbers that have a decagonal (10 sides) Voronoi cell in the Voronoi diagram of the Ulam prime spiral.
%H A257748 Vardan Semerjyan, <a href="http://smallsats.org/2014/01/03/voronoi-diagram-of-prime-spiral/">Voronoi diagram of prime spiral</a>
%o A257748 (MATLAB)
%o A257748 sz  = 701; % Size of the N x N square matrix
%o A257748 mat = spiral(sz); % MATLAB Function
%o A257748 k = 1;
%o A257748 for i =1:sz
%o A257748     for j=1:sz
%o A257748         if isprime(mat(i,j)) % Check if the number is prime
%o A257748             % saving indices of primes
%o A257748             y(k) = i; x(k) = j;
%o A257748             k = k+1;
%o A257748         end
%o A257748     end
%o A257748 end
%o A257748 xy = [x',y'];
%o A257748 [v,c] = voronoin(xy); %  Returns Voronoi vertices V and
%o A257748 % the Voronoi cells C
%o A257748 k = 1;
%o A257748 for i = 1:length(c)
%o A257748   szv = size(v(c{i},1));
%o A257748   polyN(i) = szv(1);
%o A257748   if polyN(i) == 10
%o A257748         A(k) = mat(y(i),x(i));
%o A257748         k = k+1;
%o A257748       end
%o A257748 end
%o A257748 % Print terms
%o A257748 A = sort(A);
%o A257748 fprintf('A = ');
%o A257748 fprintf('%i, ',A);
%o A257748 % When running the code be aware that the last terms you get might not be correct.
%o A257748 % They correspond to the points on the outer edges of the spiral which might be
%o A257748 % altered when considering a larger spiral.
%o A257748 % Use larger spiral to get more terms
%Y A257748 Cf. A257527, A257528, A000040.
%K A257748 nonn
%O A257748 1,1
%A A257748 _Vardan Semerjyan_, May 07 2015