[seqfan] A knight on a multiplication table

Ali Sada pemd70 at yahoo.com
Fri Nov 22 10:02:08 CET 2019


Hi Everyone,

A chess knight moves on an extended multiplication table. The knight's goal is to land on perfect numbers consecutively. It starts at 1, then tries to reach 4,8,9,16,etc. It can land on the same square multiple times.

The are two prioritized conditions here:
1) The knight must use the least number of moves between two consecutive perfect numbers.
2) The sum of numbers in the squares the knight lands on in each move should be the least.

This is the sequence generated from the process:

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, 208, 216, 208, 225, 238, 247, 252, 253, 250, 243, 196, 145, 210, 256, 270, 280, 286, 288, 286, 280, 270, 289, 304, 324
Best,
Ali



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