The following magic square has a couple unusual properties. For one, numbers appear in consecutive pairs. Also, you can connect the numbers 1 through 32 in a continuous path.
I found this in Before Sudoku. The authors attribute it to William Mannke, “A Magic Square.” Journal of Recreational Mathematics. 1 (3) page 139, July 1968.
Other magic squares:
One thought on “Consecutive pair magic square”
If you allow a path to wrap top-to-bottom and left-to-right, you can also connect 33-64 in a continuous path.