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A257748
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Prime numbers that have a decagonal (10 sides) Voronoi cell in the Voronoi diagram of the Ulam prime spiral.
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0
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8741, 9533, 11087, 14629, 17077, 26029, 29723, 33247, 38723, 40177, 43991, 45677, 56369, 57709, 58027, 68749, 77479, 81727, 88117, 90173, 93053, 110933, 112297, 112901, 114859, 117773, 127219, 129841, 131771, 146161, 156719, 159293, 169369
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OFFSET
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1,1
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LINKS
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PROG
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(MATLAB)
sz = 701; % 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) == 10
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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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