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

1,1

Links

Table of n, a(n) for n=1..48.

Vardan Semerjyan, Voronoi diagram of prime spiral

Prog

(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

Crossrefs

Cf. A257527, A257528, A000040.

Sequence in context: A154148 A340818 A242241 * A153376 A235139 A263448

Adjacent sequences: A257742 A257743 A257744 * A257746 A257747 A257748

Keyword

nonn

Author

Vardan Semerjyan, May 07 2015

Status

approved