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A257528
Prime numbers that have a quadrilateral Voronoi cell in the Voronoi diagram of the Ulam prime spiral.
8
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
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
KEYWORD
nonn
AUTHOR
Vardan Semerjyan, Apr 28 2015
STATUS
approved