A257745 Prime numbers that have a hexagonal Voronoi cell in the Voronoi diagram of the Ulam prime spiral.

5, 7, 41, 43, 89, 127, 179, 193, 233, 263, 283, 317, 379, 383, 397, 443, 457, 487, 503, 547, 599, 607, 631, 643, 647, 719, 733, 787, 809, 821, 839, 937, 947, 971, 977, 997, 1019, 1039, 1049, 1069, 1091, 1097, 1103, 1109, 1187, 1193, 1217, 1231

Offset: 1

Author

Vardan Semerjyan, May 07 2015

Keywords

• nonn

Links

• Vardan Semerjyan, Voronoi diagram of prime spiral

Crossrefs

Cf. A257527, A257528, A000040.

Programs

MATLAB

sz  = 201; % Size of the N x N square matrix
mat = spiral(sz); % MATLAB Function
k = 1;
for i =1:sz
    for j=1:sz
        if isprime(mat(i,j)) % Check if the number is prime
            % saving indices of primes
            y(k) = i; x(k) = j;
            k = k+1;
        end
    end
end
xy = [x',y'];
[v,c] = voronoin(xy); %  Returns Voronoi vertices V and
% the Voronoi cells C
k = 1;
for i = 1:length(c)
  szv = size(v(c{i},1));
  polyN(i) = szv(1);
  if polyN(i) == 6
        A(k) = mat(y(i),x(i));
        k = k+1;
      end
end
% Print terms
A = sort(A);
fprintf('A = ');
fprintf('%i, ',A);
% When running the code be aware that the last terms you get might not be correct.
% They correspond to the points on the outer edges of the spiral which might be
% altered when considering a larger spiral.
% Use larger spiral to get more terms