What binary sequence a₁,a₂,a₃,...a_n,... can be defined by the equation: (a_n)XOR (3*a_n)=a_n+1?
Provide the proof of your formula.

(In reply to one soln by Steven Lord)

The process will multiply any number by 2, so the general formula would be a0 * 2^n. If a₀ is 1/2 it gives the sequence 1, 2, 4, .... If a₀ = 1 then it gives the sequence 2, 4, 8, ....  But a₀ need not be a power of 2: if a₀ = 3 you get 6, 12, 24, ....

Posted by Charlie on 2018-10-31 10:20:18