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

1,1

Links

Table of n, a(n) for n=1..54.

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) == 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.

Crossrefs

Cf. A000040, A257528, A257527.

Sequence in context: A130796 A258578 A031924 * A240886 A162587 A033216

Adjacent sequences: A257525 A257526 A257527 * A257529 A257530 A257531

Keyword

nonn

Author

Vardan Semerjyan, Apr 28 2015

Status

approved