login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A326406 Minesweeper sequence of positive integers arranged on 2d grid along triangular maze. 7
3, -1, -1, 2, -1, 3, -1, 4, 4, 1, -1, 3, -1, 3, 2, 1, -1, 3, -1, 3, 2, 1, -1, 2, 3, 2, 3, 1, -1, 3, -1, 2, 2, 1, 2, 1, -1, 2, 3, 1, -1, 3, -1, 3, 2, 1, -1, 2, 3, 2, 3, 2, -1, 2, 1, 0, 1, 2, -1, 3, -1, 2, 2, 1, 2, 1, -1, 2, 2, 1, -1, 3, -1, 3, 4, 0, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Write positive integers on 2-d grid starting with 1 in top left corner and continue along triangular maze as in A056023.

Replace each prime by -1 and nonprimes by 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 classical Minesweeper game.

a(n) < 5 (conjectured).

Set of n such that a(n) = 4 is unbounded (conjectured).

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..11325 (150 antidiagonals).

Michael De Vlieger, Minesweeper-style graph read along original mapping, replacing -1 with a "mine", and 0 with blank space.

Michael De Vlieger, Square plot of a million terms read along original mapping, with black indicating a prime and levels of gray commensurate to a(n).

Witold Tatkiewicz, link for Java program

Wikipedia, Minesweeper game

EXAMPLE

Consider positive integers placed on the plane along triangular maze:

   1  2  6  7 15 16 ...

   3  5  8 14 17 ...

   4  9 13 18 ...

  10 12 19 ...

  11 20 ...

  21 ...

  ...

1 is not prime and in adjacent grid cells there are 3 primes: 2, 3 and 5. Therefore a(1) = 3.

2 is prime, therefore a(2) = -1.

8 is not prime and in adjacent grid cells there are 4 primes: 2, 5, 7 and 13. Therefore a(8) = 4.

Replacing n by 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:

  3  *  3  *  2  1  1  *  2  1  1  * ...

  *  *  4  3  *  3  3  3  *  2  2  2

  2  4  *  3  2  *  *  2  1  2  *  1

  1  3  *  3  2  3  3  2  1  1  1  2

  *  3  2  2  *  2  2  *  2  1  .  1

  2  *  1  1  3  *  3  2  *  2  1  1

  1  2  3  2  3  *  3  2  3  *  1  .

  1  2  *  *  3  2  2  *  2  1  2  2

  *  2  2  4  *  2  1  2  3  2  2  *

  1  1  .  2  *  3  1  1  *  *  2  3

  .  1  2  3  3  *  2  2  3  2  1  1

  1  2  *  *  2  1  2  *  1  .  .  1

...

In order to produce sequence graph is read along original mapping.

MATHEMATICA

Table[If[PrimeQ@ m, -1, Count[#, _?PrimeQ] &@ Union@ Map[s[[#1, #2]] & @@ # &, Join @@ Array[FirstPosition[s, m] + {##} - 2 &, {3, 3}]]], {m, PolygonalNumber@ n}]] (* Michael De Vlieger, Oct 02 2019 *)

PROG

(Java) See Links section.

CROSSREFS

Cf. A056023 - plane mapping

Different arrangements of integers:

Cf. A326405 - antidiagonals,

Cf. A326407 - square mapping,

Cf. A326408 - square maze,

Cf. A326409 - Hamiltonian path,

Cf. A326410 - Ulam's spiral.

Sequence in context: A107297 A107296 A080847 * A270572 A095276 A246457

Adjacent sequences:  A326403 A326404 A326405 * A326407 A326408 A326409

KEYWORD

sign,tabl

AUTHOR

Witold Tatkiewicz, Oct 02 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 21 01:03 EST 2020. Contains 332086 sequences. (Running on oeis4.)