
COMMENTS

Similar to sequence A047838.
My computer program worked as follows:
a) generate a permutation
b) place the permutation into the array
c) calculate the array position (row, column) of each integer
d) sort the integers into another array preserving row and column
e) travel the new array from 1..n^2 and summing the absolute value of the differences between the rows of consecutive integers and summing the absolute value of the differences of the columns of consecutive integers. The organization number is the sum of the two sums.
For instance, with the permutation 8, 3, 6, 5, 9, 1, 2, 7, 4 place the integers into a 3 X 3 array as such:
8 3 6
5 9 1
2 7 4
(Notice the next integer is a knight's move away. This is not the only sequence that will give an organization number of 23, but this is why I wonder if the sequence is the same as A098499.)
Then sort the integers preserving their row and column:
number, row, column
1, 2, 3
2, 3, 1
3, 1, 2
4, 3, 3
5, 2, 1
6, 1, 3
7, 3, 2
8, 1, 1
9, 2, 2
Traveling from 1 to 9, the differences in the row numbers are 1, 2, 2, 1, 1, 2, 2, 1 (a sum of 12) and the differences in the column numbers are 2, 1, 1, 2, 2, 1, 1, 1 (a sum of 11) therefore the organization number is 23.
This is basically a traveling salesman variant.  D. S. McNeil, Aug 26 2010
