A023406 If any even power of 2 ends with k 1's and 6's, they must be the first k elements of this sequence in reverse order.

6, 1, 6, 1, 1, 1, 6, 1, 6, 1, 6, 6, 1, 6, 6, 6, 6, 6, 6, 1, 6, 1, 1, 1, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6, 6, 1, 6, 6, 6, 6, 6, 1, 1, 1, 1, 6, 6, 1, 6, 1, 1, 6, 1, 1, 6, 1, 1, 6, 1, 1, 1, 1, 6, 1, 1, 6, 1, 6, 6, 6, 1, 1, 6, 6, 6, 1, 6, 6, 6, 1, 1, 1, 1, 1, 6, 1, 1, 6, 6, 6, 1, 6, 1, 6, 6, 1, 6, 1, 6, 6, 1, 1, 1, 1, 1, 6, 1, 1