

A257745


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


1



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
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OFFSET

1,1


LINKS



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



KEYWORD

nonn


AUTHOR

Vardan Semerjyan, May 07 2015


STATUS

approved



