A088975 Breadth-first traversal of the Collatz tree, with the odd child of each node traversed prior to its even child. If the Collatz 3n+1 conjecture is true, this is a permutation of all positive integers.

1, 2, 4, 8, 16, 5, 32, 10, 64, 3, 20, 21, 128, 6, 40, 42, 256, 12, 13, 80, 84, 85, 512, 24, 26, 160, 168, 170, 1024, 48, 52, 53, 320, 336, 340, 341, 2048, 96, 17, 104, 106, 640, 672, 113, 680, 682, 4096, 192, 34, 208, 35, 212, 213, 1280, 1344, 226, 1360, 227, 1364