This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A326408 #25 Jun 19 2025 09:19:28
%S A326408 2,-1,-1,3,-1,3,-1,4,3,1,-1,4,-1,3,4,2,-1,2,-1,2,3,3,-1,2,1,0,2,3,-1,
%T A326408 2,-1,2,2,1,3,2,-1,1,1,2,-1,4,-1,2,3,3,-1,1,0,0,2,3,-1,1,1,1,3,3,-1,3,
%U A326408 -1,2,2,1,0,1,-1,3,3,2,-1,2,-1,2,1,0,1,2,-1,2,1
%N A326408 Minesweeper sequence of positive integers arranged on a 2D grid along a square maze.
%C A326408 Place positive integers on 2D grid starting with 1 in the top left corner and continue along the square maze as in A081344.
%C A326408 Replace each prime with -1 and each nonprime with the number of primes in adjacent grid cells around it.
%C A326408 n is replaced by a(n).
%C A326408 This sequence treats prime numbers as "mines" and fills gaps according to the rules of the classic Minesweeper game.
%C A326408 a(n) < 5.
%C A326408 Set of n such that a(n) = 4 is unbounded (conjectured).
%H A326408 Michael De Vlieger, <a href="/A326408/b326408.txt">Table of n, a(n) for n = 1..10000</a>
%H A326408 Michael De Vlieger, <a href="/A326408/a326408.png">Minesweeper-style graph</a> read along original mapping, replacing -1 with a "mine", and 0 with blank space.
%H A326408 Michael De Vlieger, <a href="/A326408/a326408_1.png">Square plot of a million terms</a> read along original mapping, with black indicating a prime and levels of gray commensurate to a(n).
%H A326408 Witold Tatkiewicz, <a href="https://pastebin.com/dWGN3SrE">link for Java program</a>
%H A326408 Wikipedia, <a href="https://en.wikipedia.org/wiki/Minesweeper_(video_game)">Minesweeper game</a>
%e A326408 Consider positive integers distributed onto the plane along increasing square array:
%e A326408 1 4 5 16 17 36 ...
%e A326408 2 3 6 15 18 35
%e A326408 9 8 7 14 19 34
%e A326408 10 11 12 13 20 33
%e A326408 25 24 23 22 21 32
%e A326408 26 27 28 29 30 31
%e A326408 ...
%e A326408 1 is not prime and in adjacent grid cells there are 2 primes: 2 and 3. Therefore a(1) = 2.
%e A326408 2 is prime, therefore a(2) = -1.
%e A326408 8 is not prime and in adjacent grid cells there are 4 primes: 2, 3, 7 and 11. Therefore a(8) = 4.
%e A326408 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:
%e A326408 2 3 * 2 * 2 * 1 . 1 * 1 ...
%e A326408 * * 3 4 2 3 1 2 1 3 2 2
%e A326408 3 4 * 3 * 1 1 2 * 3 * 1
%e A326408 1 * 4 * 2 2 2 * 3 * 2 2
%e A326408 1 2 * 3 3 2 * 3 3 1 2 2
%e A326408 . 2 3 * 2 * 4 * 2 2 2 *
%e A326408 . 1 * 3 3 2 * 3 * 2 * 4
%e A326408 . 2 3 * 1 1 1 3 2 4 3 *
%e A326408 1 2 * 2 1 . 1 2 * 2 * 2
%e A326408 1 * 2 1 . . 1 * 3 3 1 1
%e A326408 1 1 1 . 1 1 2 2 * 2 1 .
%e A326408 . 1 1 1 1 * 2 2 2 * 1 1
%e A326408 ...
%e A326408 In order to produce the sequence, the graph is read along its original mapping.
%t A326408 Block[{n = 9, s}, s = ArrayPad[Array[If[#1 < 2 #2 - 1, #2^2 + #2 - #1, (#1 - #2)^2 + #2] & @@ {#1 + #2 - 1, #2} & @@ If[Or[And[#2 < #1, EvenQ@ #1], And[#1 < #2, EvenQ@ #2]], {#1, #2}, {#2, #1}] &, {# + 1, # + 1}], 1] &@ n; Table[If[PrimeQ@ m, -1, Count[#, _?PrimeQ] &@ Union@ Map[s[[#1, #2]] & @@ # &, Join @@ Array[FirstPosition[s, m] + {##} - 2 &, {3, 3}]]], {m, n^2}]] (* _Michael De Vlieger_, Oct 04 2019 *)
%o A326408 (Java) // See Links section.
%Y A326408 Cf. A081344 - plane mapping
%Y A326408 Different arrangements of integers:
%Y A326408 Cf. A326405 - antidiagonals,
%Y A326408 Cf. A326406 - triangle maze,
%Y A326408 Cf. A326407 - square mapping,
%Y A326408 Cf. A326409 - Hamiltonian path,
%Y A326408 Cf. A326410 - Ulam's spiral.
%K A326408 sign,tabl
%O A326408 1,1
%A A326408 _Witold Tatkiewicz_, Oct 04 2019