Can you fill in the blanks in the following sequence?
1,1,4,2,7,3,17,4,20,?,37,6,47,5,51,?,61,3,70,3,9?,2,100,1
I've been over this one in every way I can think to look at it and even enlisted the aid of my roommate who is as stumped as I am. Looking forward to seeing the solution.