

A326410


Minesweeper sequence of positive integers arranged on square spiral on 2d grid.


7



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

1,1


COMMENTS

Place positive integers on 2d grid starting with 1 in the centre and continue along spiral.
Replace primes by 1 and nonprimes by the number of primes in adjacent grid cells around them.
n is replaced by a(n).
This sequence treats prime numbers as "mines" and fills gaps according to classical Minesweeper game.
a(n) = 5 for n = 12.
Set of n such that a(n) = 4 is unbounded (conjecture).


LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10201 (51 spiral iterations).
Michael De Vlieger, Minesweeperstyle graph read along original mapping, replacing 1 with a "mine", and 0 with blank space.
Michael De Vlieger, Square plot of 10^3 spiral iterations read along original mapping, with black indicating a prime and levels of gray commensurate to a(n).
Wikipedia, Minesweeper game


EXAMPLE

Consider positive integers distributed onto the plane along the square spiral:
.
37363534333231
 
38 1716151413 30
   
39 18 543 12 29
     
40 19 6 12 11 28
    
41 20 78910 27
  
42 212223242526

43444546474849...
.
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:
*22133*
 
3 *222* 3
   
3 3 *3* 5 *
     
2 * 3 4* * 3
    
* 3 *332 2
  
3 32*21.

*112*21...
In order to produce the sequence graph is read along the square spiral.


CROSSREFS

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:
Cf. A326405 (antidiagonals), A326406 (triangle maze), A326407 (square mapping), A326408 (square maze), A326409 (Hamiltonian path).
Sequence in context: A293770 A111311 A327893 * A255235 A293882 A016524
Adjacent sequences: A326407 A326408 A326409 * A326411 A326412 A326413


KEYWORD

sign,tabl


AUTHOR

Witold Tatkiewicz, Oct 07 2019


STATUS

approved



