1. 1/16 x 1 000 000= 62500
2. Each half life is 5750 years long
3. The end of a half life is found by dividing the beginning of the half life by 2.
4. The number 62500 is between the 7th and the 8th half lives (refer to the number of 14C atoms on my table)
5. The 7th half life is 40250 years, and the 8th half life is 46000 years.
6. Therefore, your estimate would be a number roughly in the middle of 40250 and 46000 (for example: 43000)
Hope this helps :)