[seqfan] Re: A puzzle from Emissary

[Graeme McRae]

One way to generalize this "number of steps needed to get to 1" sequence  to other bases, b, is as follows...

The base b sequence a_b(n) is the least number of steps it takes to get from (b-1)*n to (b-1), interpreting all numbers in base b for the purpose of evaluating the expressions containing plus signs.  

The 1's in this sequence would be for numbers of the form

90000...0

Where "9" represents b-1, and the 2's in this sequence include (but are not limited to) numbers of the form

899999...1, 

where "8" represents b-2. 

--Graeme McRae,
Palmdale, CA