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Let a1=1a_1=1a1=1 and for each positive integer nnn, an+1=an+⌊an⌋a_{n+1}=a_n+\left \lfloor \sqrt{a_n} \right \rflooran+1=an+⌊an⌋.
Is it true or false that for infinite many positive integers kkk, aka_kak is a power of 2?
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