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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..54.

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) == 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

Cf. A000040, A257528, A257527.

Sequence in context: A130796 A258578 A031924 * A240886 A162587 A033216

Adjacent sequences:  A257525 A257526 A257527 * A257529 A257530 A257531

KEYWORD

nonn

AUTHOR

Vardan Semerjyan, Apr 28 2015

STATUS

approved

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Last modified November 13 23:48 EST 2019. Contains 329106 sequences. (Running on oeis4.)