Here is a sequence :

01 10 1001 10010110 1001011001101001 .....

Let us write the same sequence without spaces

01101001100101101001011001101001 ....

Starting from left to right and replacing each digit one by its rank

2 3 5 8 9 12 14 15 17

Can you find the formula to compute the sum S(n) where n is nth digit 1?

Example :

S(5)=2+3+5+8+9=27

S(6)=27+12=39

S(7)=39+14=53

and so on