Does the decimal portion of $n\log_3 2$ include all irrational numbers between 0 and 1 repeatedly, where $n$ is all positive integers?
Oddly enough I ran into this question while fooling around with the Collatz Conjecture.
Lacking an answer, directions as to how to find an answer (what to read up on) would be useful.
Decimal Portion: integer portion →
3 | .141592653 ← decimal portion
repeatedly: cycling through again and again
As a follow-up question, and perhaps the one I should have initially asked:
Would the decimal portion of $n\log_3 2$ include all numbers in the decimal portion of $log_3(n + 1/2)$? (again, n representing all positive integers)