Sum of ones

def bit_recur(n):
    if n == 0:
        return 0
    k = 0
    while (1 << (k + 1)) <= n:
        k += 1
    largest_power = 1 << k  #power of 2
    
    #half are 1, k * 2^(k-1)
    bits_full = k * (1 << (k - 1)) if k > 0 else 0
    
    #remaining
    front_ones = n - largest_power + 1
    leftover_ones = bit_recur(n - largest_power)

    return bits_full + front_ones + leftover_ones

n = int(input())
print(bit_recur(n))

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED