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A326410
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Minesweeper sequence of positive integers arranged on a square spiral on a 2D grid.
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7
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4, -1, -1, 3, -1, 3, -1, 3, 3, 2, -1, 5, -1, 2, 2, 2, -1, 3, -1, 3, 3, 2, -1, 2, 1, 0, 2, 3, -1, 3, -1, 3, 3, 1, 2, 2, -1, 3, 3, 2, -1, 3, -1, 1, 1, 2, -1, 2, 1, 1, 1, 1, -1, 2, 3, 2, 2, 2, -1, 2, -1, 2, 2, 1, 3, 3, -1, 1, 2, 3, -1, 4, -1, 3, 2, 0, 1, 2, -1, 1, 1
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OFFSET
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1,1
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COMMENTS
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Place positive integers on a 2D grid starting with 1 in the center and continue along a spiral.
Replace each prime with -1 and each nonprime with the number of primes in adjacent grid cells around it.
n is replaced by a(n).
This sequence treats prime numbers as "mines" and fills gaps according to the rules of the classic Minesweeper game.
a(n) = 5 for n = 12.
Set of n such that a(n) = 4 is unbounded (conjecture).
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LINKS
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Michael De Vlieger, Minesweeper-style graph read along original mapping, replacing -1 with a "mine", and 0 with blank space.
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EXAMPLE
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Consider positive integers distributed onto the plane along the square spiral:
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37--36--35--34--33--32--31
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38 17--16--15--14--13 30
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39 18 5---4---3 12 29
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40 19 6 1---2 11 28
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41 20 7---8---9--10 27
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42 21--22--23--24--25--26
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43--44--45--46--47--48--49--...
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1 is not prime and in adjacent grid cells there are 4 primes: 2, 3, 5 and 7. Therefore a(1) = 4.
2 is prime, therefore a(2) = -1.
8 is not prime and in adjacent grid cells there are 4 primes: 2, 7 and 23. Therefore a(8) = 3.
Replacing n with a(n) in the plane described above, and using "." for a(n) = 0 and "*" for negative a(n), we produce a graph resembling Minesweeper, where the mines are situated at prime n:
*---2---2---1---3---3---*
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3 *---2---2---2---* 3
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3 3 *---3---* 5 *
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2 * 3 4---* * 3
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* 3 *---3---3---2 2
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3 3---2---*---2---1---.
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*---1---1---2---*---2---1---...
In order to produce the sequence, the graph is read along the square spiral.
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CROSSREFS
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Cf. A136626 - similar sequence: For every number n in Ulam's spiral the sequence gives the number of primes around it (number n excluded).
Cf. A136627 - similar sequence: For every number n in Ulam's spiral the sequence gives the number of primes around it (number n included).
Different arrangements of integers:
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KEYWORD
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AUTHOR
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STATUS
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approved
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