[seqfan] Re: A puzzle from Emissary

Graeme McRae g_m at mcraefamily.com
Wed Nov 30 20:26:55 CET 2011

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


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


where "8" represents b-2. 

--Graeme McRae,
Palmdale, CA

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