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A257749 Prime numbers that have a dodecagonal (12 sides) Voronoi cell in the Voronoi diagram of the Ulam prime spiral. 0
61673, 635939, 706117, 720743, 1483439, 1742501, 1766701, 1847603, 2097959, 2163461, 2365289, 2429411, 3420101, 3490703, 3657361, 3920843, 3973829, 4758973, 4920887, 4989779, 5273753, 6167687, 6223247, 6573559, 6655409, 6694333, 6791881, 7095503, 7102349, 7338293, 7644541 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..31.

Vardan Semerjyan, Voronoi diagram of prime spiral

PROG

(MATLAB)

sz  = 3001; % 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) == 12

        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

Cf. A257527, A257528, A000040.

Sequence in context: A237013 A340438 A253613 * A340126 A112015 A234864

Adjacent sequences:  A257746 A257747 A257748 * A257750 A257751 A257752

KEYWORD

nonn

AUTHOR

Vardan Semerjyan, May 07 2015

STATUS

approved

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Last modified May 20 01:04 EDT 2022. Contains 353847 sequences. (Running on oeis4.)