Let the function O(n) denote the sum of natural numbers, i, less than or equal to n. However, this function has one trick - if the number to be added, i, is a power of 2, then instead of adding we subtract the number.

Find O(4)+O(5)+O(6)+...+O(10000)

function written in Python:

def OhSum(a, b):
    exponent = 0
    powersOfTwo = []    # make a list [0, 1, 2, 4, 8, ...]
    OhList = []         # make a list [0, O(1), O(2), O(3), ...]
    OhList.append(0)    # now OhList[0] = 0
    
    while b+1 > 2**exponent:
        powersOfTwo.append(2**exponent)
        exponent += 1
  
    for i in range(1, b+1):
        if i in powersOfTwo:
            OhList.append(OhList[i-1] - i)
        else:
            OhList.append(OhList[i-1] + i)

    mySum = 0
    for i in range(a, b+1):
        mySum = mySum + OhList[i]
    return format(mySum, ',')
-------------------------
OhSum(4, 10000)
166,567,934,208 

Posted by Larry on 2019-10-14 18:00:07