Magic Numbers

A positive integer is $$magic$$ if$,$ and only if$,$ it can be reduced to $1$ by repeatedly dividing it by $2$ if it$$s

even or multiplying it by $3$ and then adding $1$ if it$$s odd. One is magic by definition. Two is even and

$2/2=1.$ So$,$ for a better example, $3$ is magic because $3$ reduces first to $10(3*3+1),$ then to $5(10/2),$ then

to $16(5*3+1),$ then to $8(16/2),$ then to $4(8/2),$ then to $2(4/2),$ and finally to $1(2/2).$ Mikes magic

numbers hypothesis states that all positive integers are magic, or$,$ formally: $$x in Z$,$ MAGIC$($x$)$ where

MAGIC$($x$)$ is the predicate $$x is magic$$