Happy trails to you

One of my current preoccupations is the extension of an idea that Eric Angelini mentioned to Sequence Fanatics eleven days ago. I wondered what would happen if we allowed the "digit trail" of a negative number to be the negatives of that number's digits. For starting numbers greater than ten, this had the resulting sequence oscillate between negative and positive territory, with each "run" taking another shot at hitting zero. The number of steps needed to get to the first zero is A208059. I subsequently extended the concept to other bases. Eric did a nice job of summarizing (in French) all of this.