The game involves N coins and a player can flip any consecutive $K$ sequence of coins, where $K$ is a perfect square.
I have developed a function to list the values, but I am looking for a mathematical way of expressing the SG-value of the coin in the $j$-th position. I have tried, but the values seem arbitrary. How could I find this function? Is it possible?
The first 580 S-G values are as follows:
1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 3 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 3 1 2 1 4 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 3 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 3 1 2 1 5 1 1 1 2 1 1 1 8 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 3 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 3 1 2 1 4 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 3 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 3 1 2 1 5 1 1 1 2 1 1 1 8 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 3 4 1 1 1 2 1 1 1 2 1 1 1 3 6 1 3 1 5 1 1 2 1 1 1 2 1 1 1 4 1 1 1 3 1 1 1 2 3 1 5 1 1 1 4 1 1 2 1 1 1 5 1 1 2 1 1 8 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 4 1 1 1 2 1 1 3 5 9 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 5 1 3 2 1 1 1 2 1 1 1 8 1 1 1 2 1 1 1 2 1 1 3 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 3 4 1 1 1 10 1 3 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 4 3 2 1 1 1 5 4 1 1 7 2 1 5 2 1 1 3 1 1 1 3 1 2 1 4 1 1 1 2 1 1 1 4 9 1 1 1 5 1 1 2 1 1 1 3 1 2 1 1 6 2 1 1 1 2 1 1 1 4 1 1 1 2 1 1 3 7 2 1 2 9 1 1 1 7 6 2 1 1 3 4 1 1 1 2 1 1 1 11 1 3 1 1 1 2 1 1 6 1 1 2 1 3 4 1 1 2 1 1 1 9 2 1 1 1 5 1 1 1 11 6 1 2 1 4 1 2 3 1 1 5 2 1 1 1 2 1 1 3 4 1 1 3 1 2 1 1 1 2 1 4 2 4 1 6 12 2 2 1 6 4 1 1 3 1 4 1 9 1 11 2 1 1 1 2 3 1 1 1 2 1 1 1 3 5 3 1 1 1 5 1 1 1 5 1 1 4 7 1 1 3 2 1 1 1 2 1 1 1 2 1 1 1 3 8 1 1 3 2 1 5 1 1 1 3 5 4 1 1 6 11 4 13 12 13 1 1 1 3 16 1 1 1 2 1