A085240 As exponents in powers of 2 or 3 (A006899) occur in A085238 exactly twice, a self-inverse permutation of natural numbers is induced.

2, 1, 5, 7, 3, 10, 4, 12, 15, 6, 18, 8, 20, 23, 9, 25, 28, 11, 31, 13, 33, 36, 14, 38, 16, 41, 43, 17, 46, 49, 19, 51, 21, 54, 56, 22, 59, 24, 62, 64, 26, 67, 27, 69, 72, 29, 74, 77, 30, 80, 32, 82, 85, 34, 87, 35, 90, 93, 37, 95, 98, 39, 100, 40, 103, 105, 42, 108