A257528 Prime numbers that have a quadrilateral Voronoi cell in the Voronoi diagram of the Ulam prime spiral.

23, 31, 47, 59, 71, 73, 79, 131, 139, 167, 173, 181, 229, 239, 251, 269, 277, 331, 353, 359, 367, 421, 439, 449, 467, 479, 499, 587, 617, 661, 701, 709, 739, 751, 761, 797, 887, 941, 967, 1021, 1063, 1129, 1151, 1171, 1181, 1229, 1279, 1291, 1303, 1321, 1427, 1429, 1451, 1481

Offset: 1

Author

Vardan Semerjyan, Apr 28 2015

Keywords

• nonn

Links

• Vardan Semerjyan, Voronoi diagram of prime spiral

Crossrefs

Cf. A000040, A257528, A257527.

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) == 4
        A(k) = mat(y(i),x(i));
        k = k+1;
      end
end
% Print terms
A = sort(A);
fprintf('A = ');
fprintf('%i, ',A);
% Note that the last terms 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 a larger spiral to get more terms.