counting

Jason counts up from 1 to 9 skipping the even numbers, and then immediately counts down without skipping any of the numbers, and then back up to 9 skipping the evens, and so on, alternately counting up and down

$(1, 3,5,7,9,8,7,6,5,4,3,2,1,3,5,\ldots )$

What is the $1000^{th}$ integer in his list?