Find sum of the digits of: 2023²⁰²³

For example, the sum of digits of 2¹⁶= 65536 is 6+5+5+3+6 =25

First, find the digital root.
The digital root of 2023 is 7
The digital root of a base to a power follows a pattern.
When the base has a digital root of 7, the pattern had a cycle length of 3 and is {7,4,1,7,4,1, ...}
The exponent 2023 is 1 mod 3.
So the digital root of 2023^2023 is the same as the digital root of 7**1
The digital root of 2023^2023 is 7.

I searched for a pattern in sum of digits of powers of 2023 but without success.

So I was unable to find a clever solution, although by direct calculation the answer is 30112.

sod(2023**2023)
Out[2]: 30112

--------
def sod(n):
    """ Input an integer.  Returns the Sum of the Digits  """
    aList = list(str(n))
    ans = 0
    for c in aList:
        ans = ans + int(c)
    return ans

Posted by Larry on 2023-10-27 12:42:51