A327602 A chess knight starts at 1 on an extended multiplication table and moves to the next perfect power such that 1) the number of jumps is minimized and 2) the sum of the intermediate numbers is minimized. In case of a tie, choose the lexicographically earliest path.

1, 6, 15, 4, 12, 8, 12, 4, 9, 10, 16, 18, 25, 28, 27, 14, 32, 18, 16, 36, 21, 30, 49, 54, 64, 70, 81, 88, 100, 108, 121, 108, 91, 90, 85, 76, 63, 92, 125, 78, 56, 90, 128, 102, 144, 102, 64, 90, 112, 130, 144, 154, 160, 162, 160, 154, 169, 180, 196

Offset: 1

Author

Ali Sada, Dec 02 2019

Keywords

• nonn

Examples

			Between 4 and 8, the shortest route is through 12 (2*6); it takes only two steps:
.
      1      2      3      4      5      6      7      8
  +------+------+------+------+------+------+------+------+
  |      |      |      |      |      |      |      |      |
1 |   1  |   2  |   3  |  *4* |   5  |   6  |   7  | .*8* |
  |      |      |      |      |.     |      |    . |      |
  +------+------+------+------+---.--+------+-.----+------+
  |      |      |      |      |      .     .|      |      |
2 |   2  |   4  |   6  |   8  |  10  | *12* |  14  |  16  |
  |      |      |      |      |      |      |      |      |
  +------+------+------+------+------+------+------+------+
  |      |      |      |      |      |      |      |      |
3 |   3  |   6  |   9  |  12  |  15  |  18  |  21  |  24  |
  |      |      |      |      |      |      |      |      |
  +------+------+------+------+------+------+------+------+
  |      |      |      |      |      |      |      |      |
4 |   4  |   8  |  12  |  16  |  20  |  24  |  28  |  32  |
  |      |      |      |      |      |      |      |      |
  +------+------+------+------+------+------+------+------+
.
Between 32 and 36, there are several routes that take only three jumps. We choose 32,18,16,36 because the sum of intermediate numbers is the least.
		

Crossrefs

Cf. A316588, A316328.