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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.
0
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
1,2
EXAMPLE
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
Sequence in context: A328339 A019306 A115408 * A105052 A003566 A349083
KEYWORD
nonn
AUTHOR
Ali Sada, Dec 02 2019
STATUS
approved