A269867 Self-inverse permutation of natural numbers: a(1) = 1, for even n, a(n) = A250469(1+a(n/2)), for odd n, a(n) = 2*a(A268674(n)-1).

1, 3, 2, 9, 6, 5, 18, 27, 4, 11, 10, 15, 22, 23, 12, 81, 30, 7, 162, 33, 36, 13, 14, 45, 54, 29, 8, 69, 26, 17, 138, 243, 20, 37, 46, 21, 34, 167, 44, 99, 42, 41, 198, 39, 24, 35, 82, 135, 90, 91, 60, 87, 70, 25, 66, 207, 324, 65, 174, 51, 130, 149, 72, 729, 58, 55, 102, 111, 28, 53, 110, 63, 106, 77, 108, 501, 74, 115, 126, 297, 16, 47