1,2,4,3,6,5,10,7,14,8,16,9,18,11,22,12,24...

This sequence has simple rules with a major hint in the title.

Part 1) Determine the rule to extend the sequence.

Part 2) Find, with no aids beyond a simple calculator, the 1000th term of this sequence.

The rule seems to be to double the previous entry until one or more gaps exist in the sequence. At that point insert the first missing number, then start the doubling again. This quickly becomes an alternation of doubling and filling in, as it doesn't seem the case that doubling fails to leave a gap except at the very beginning. 

Edited on July 25, 2016, 10:19 am

Posted by Charlie on 2016-07-25 10:17:43