A351686 Solution to stepping stone puzzle if we start with one 1 and n 2's for consecutive primes.

13, 23, 31, 41, 53, 61, 73, 97, 103

Offset

1,1

Comments

Start with an infinite square grid. Each cell has eight neighbors. Place one 1 and n 2's anywhere. Now place the prime numbers 3, 5, 7, ..., m in order, subject to the rule that when you place k, the sum of its neighbors must equal k. Then a(n) is the maximum m that can be achieved.

Links

Table of n, a(n) for n=1..9.

Rodolfo Kurchan, Puzzle Fun, Forest of Numbers.

Carlos Rivera, Puzzle 1079. Forest of Prime Numbers, The Prime Puzzles & Problems Connection, March 2022.

Example

Illustration for a(1) with 1 stone = 13 from Rodolfo Kurchan
   .  .  1
   . 11  3
  13  2  5
   .  .  7
a(2) with 2 stones = 23 from Rodolfo Kurchan
   .  .  1 23  .
   . 11  3  . 19
  13  2  5 17  2
   .  .  7  .  .
a(3) with 3 stones = 31 from Rodolfo Kurchan
   .  .  1 23  .
   . 11  3  . 19
  13  2  5 17  2
   . 29  7 31  .
   2  .  .  .  .
a(4) with 4 stones = 41 from Dmitry Kamenetsky
   .  2 37 31  .  1  .
  23  2  .  2 29  .  3
   . 19 17 13 11  2  5
   .  .  . 41  .  7  .
a(5) with 5 stones = 53 from Giorgio Vecchi
  -- 47 -- 31 --
  43 02 02 29 --
  41 -- 23 03 01
  02 37 05 11 --
  -- 07 -- 02 13
  -- -- -- 17 53
  -- -- -- 19 02
a(6) with 6 stones = 61 from Giorgio Vecchi
  -- -- -- 31 02 02 61 --
  -- -- -- -- 29 -- 59 --
  -- 47 37 23 -- 02 53 02
  03 02 05 07 11 13 17 19
  -- 01 -- 02 -- 41 -- --
  -- -- -- -- 43 -- -- --
a(7) with 7 stones = 73 from Giorgio Vecchi
  -- -- -- -- -- -- 61 -- 47 -- --
  -- 07 -- 71 -- 59 -- 02 02 43 02
  02 05 41 13 17 19 23 29 02 37 --
  -- 03 11 02 53 02 73 -- 31 -- --
  -- -- 01 67 -- -- -- -- -- -- --
a(8) with 8 stones = 89 from Giorgio Vecchi
  -- -- -- -- 19 02 73 -- --
  -- -- -- -- 17 -- -- 71 --
  -- -- 29 13 02 23 02 67 02
  07 05 11 59 -- 31 02 61 --
  -- 02 03 01 -- 37 02 53 --
  -- -- 89 83 79 41 02 47 --
  -- -- -- -- -- -- 43 -- --
a(9) with 9 stones = 97 from Dmitry Kamenetsky
  -- -- -- -- -- 61 -- --
  -- -- -- -- -- 59 02 --
  -- -- -- 67 02 02 53 19
  -- 02 11 47 07 13 17 89
  -- 05 03 01 23 02 -- --
  -- -- 71 29 -- -- -- --
  -- 73 02 31 97 -- -- --
  -- 79 -- 37 -- -- -- --
  02 83 02 41 02 -- -- --
  -- -- -- -- 43 -- -- --
a(10) with 10 stones = 103 from Giorgio Vecchi
-- -- -- -- 103 02 --
-- -- -- -- 101 -- 47
-- 02 -- 97 -- 02 43
-- 23 29 31 37 41 --
19 02 -- 02 -- 02 --
17 53 59 61 67 02 --
13 02 -- -- -- 71 --
11 -- 05 89 02 73 --
02 07 -- 03 79 -- --
-- -- -- 83 01 -- --

Crossrefs

Cf. A337663.

Sequence in context: A342253 A296806 A143788 * A165459 A108794 A272721

Adjacent sequences: A351683 A351684 A351685 * A351687 A351688 A351689

Keyword

nonn,more

Author

Rodolfo Kurchan, May 04 2022

Status

approved