A certain bacterium propagates itself by subdividing, creating four additional bacteria, each identical to the parent bacterium. If the bacteria subdivide in this manner n times, then, assuming that none of the bacteria die, the number of bacteria present after each subdivision is given by the sequence

where

Three such bacteria subdivide n times and none of the bacteria die. The total number of bacteria is then 1 048 575. How many times did the bacteria divide?

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