Sum of Digits in Base- 2 2

Number Theory Level pending

The binary expansion of the integer 23 23 is 1011 1 2 10111_2 . The sum of digits in the binary expansion of 23 23 is, s 23 = ( 1 + 0 + 1 + 1 + 1 ) = 4. s_{23} = (1+0+1+1+1)=4.

Find the sum of all positive integer n 100 n \leq 100 such that─ s ( 2 n 1 ) s n + s ( n 1 ) \large s_{(2n-1)} \neq s_{\color{#20A900}n} + s_{\color{#3D99F6} (n-1)}


Note : 2 n 1 = n + ( n 1 ) 2n-1 = {\color{#20A900}n} + {\color{#3D99F6}(n-1)} .

Assumption : If you think, there is no such n n , submit 0 0 as answer.


The answer is 4923.

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