Approximate the perfect fifth
05AB1E, 19 18 bytes

µ¯ßNLN/3.²&lt;αßDˆ›D–


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µ                      # repeat until counter == input
 ¯                     #  push the global array
  ß                    #  get the minimum (let's call it M)
   N                   #  1-based iteration count
    L                  #  range 1..N
     N/                #  divide each by N
       3.²             #  log2(3)
          &lt;            #  -1
           α           #  absolute difference with each element of the range
            ß          #  get the minimum
             Dˆ        #  add a copy to the global array
               ›       #  is M strictly greater than this new minimum?
                D–     #  if true, print N
                       #  implicit: if true, add 1 to the counter