A257527 Prime numbers that have a triangular Voronoi cell in the Voronoi diagram of the Ulam prime spiral.

313, 389, 1283, 1399, 1669, 1787, 2087, 2143, 2713, 2801, 3469, 4091, 4787, 4789, 4903, 4933, 5867, 6037, 6869, 8111, 8627, 9419, 9439, 11701, 11971, 12043, 13229, 13693, 13829, 14591, 16139, 16229, 17027, 17749, 17791, 20611, 20773

Offset

1,1

Links

Table of n, a(n) for n=1..37.

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) == 3
        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 larger spiral to get more terms

Crossrefs

Cf. A000040, A257528, A257529.

Sequence in context: A088282 A068687 A093808 * A142745 A328056 A142951

Adjacent sequences: A257524 A257525 A257526 * A257528 A257529 A257530

Keyword

nonn

Author

Vardan Semerjyan, Apr 28 2015

Status

approved