# Are you smarter than a 8th grader?

Logic Level 5

Define a sequence of natural number $${X(n)}$$ , where $$n$$ is any natural number, in which each digit of $$X(n)$$ is either $$0$$ or $$1$$, by the following rules:

$$1. X(1) = 1$$

$$2.$$ We define $$X(n+1)$$ as a natural number, which can be obtained by replacing the digits of $$X(n)$$ with $$1$$ if the digit is $$0$$, and with $$10$$ if the digit is $$1$$.

For example, $$X(1)=1$$, $$X(2)=10$$, $$X(3)=101$$, $$X(4)=10110$$ and so on.

$$A(n)$$ is defined as the number of digits in $$X(n)$$.

$$B(n)$$ is defined as the number of times $$01$$ appears in $$X(n)$$.

For example, $$B(1)=0$$, $$B(2)=0$$, $$B(3)=1$$, $$B(4)=1$$, $$B(5)=3$$ and so on.

What is $$A(23)+B(23)$$?







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