Proposed seq: base 3 analogue of A037015

[Jonathan Post]

 0, 1, 2, 4, 12, 13, 14, 24, 25, 26, 39, 40, 41, 78, 79, 80, 120, 121, 121, 125

Reading base 3 expansion from right to left, run lengths strictly increase.

This is to A037015 as A007089 is to A007088.

Or, if the "3" is arbitrary, something with the array
A[k,n] = n-th integer such that reading base k expansion from right to
left, run lengths strictly increase.