A257747 Prime numbers that have an octagonal (8 sides) Voronoi cell in the Voronoi diagram of the Ulam prime spiral.

67, 491, 613, 1013, 1117, 1201, 1249, 1301, 1373, 1543, 1753, 1907, 2017, 2339, 2411, 2657, 2671, 2879, 3023, 3037, 3181, 3677, 3727, 3733, 4139, 4409, 4549, 4861, 5303, 5381, 5399, 5857, 5897, 6301, 6373, 6737, 7433, 7499, 7577, 7583

Offset

1,1

Links

Table of n, a(n) for n=1..40.

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) == 8
        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: A142735 A342803 A219736 * A163150 A120717 A200963

Adjacent sequences: A257744 A257745 A257746 * A257748 A257749 A257750

Keyword

nonn

Author

Vardan Semerjyan, May 07 2015

Status

approved