A257529 Prime numbers that have a pentagonal Voronoi cell in the Voronoi diagram of the Ulam prime spiral.

2, 3, 11, 13, 17, 19, 29, 37, 53, 83, 97, 101, 103, 107, 109, 113, 137, 149, 151, 163, 191, 197, 211, 223, 227, 241, 257, 271, 281, 293, 307, 337, 347, 373, 401, 419, 431, 433, 461, 521, 523, 541, 563, 569, 571, 577, 593, 619, 653, 659, 673

Offset

1,1

Links

Table of n, a(n) for n=1..51.

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) == 5
        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. A257527, A257528, A000040, A077800.

Sequence in context: A082618 A020610 A351682 * A030482 A019366 A045334

Adjacent sequences: A257526 A257527 A257528 * A257530 A257531 A257532

Keyword

nonn

Author

Vardan Semerjyan, Apr 28 2015

Status

approved