A118012 a(n) = 4*A117384(n) - n; a self-inverse permutation of the natural numbers.

3, 6, 1, 8, 11, 2, 13, 4, 15, 18, 5, 20, 7, 22, 9, 24, 27, 10, 29, 12, 31, 14, 33, 16, 35, 38, 17, 40, 19, 42, 21, 44, 23, 46, 25, 48, 51, 26, 53, 28, 55, 30, 57, 32, 59, 34, 61, 36, 63, 66, 37, 68, 39, 70, 41, 72, 43, 74, 45, 76, 47, 78, 49, 80, 83, 50, 85, 52, 87, 54, 89, 56