A065189 "Greedy Queens" permutation of the natural numbers, inverse of A065188.
1, 4, 2, 5, 3, 10, 13, 11, 6, 15, 7, 20, 8, 21, 9, 26, 29, 27, 12, 31, 34, 14, 38, 40, 16, 43, 17, 42, 18, 49, 19, 50, 54, 56, 22, 59, 23, 58, 24, 64, 25, 67, 69, 71, 28, 75, 77, 30, 80, 78, 32, 85, 33, 86, 90, 35, 91, 36, 95, 37, 99, 101, 39, 104, 102, 41, 108, 111, 113, 44
Offset: 1