Given that:
- A = 20232023
- B = sod(A)
- C = sod(B)
- D = sod(C)
Determine the value of
sod(D).
*** sod(x) denotes the sum of the digits of x.
For example: sod(38) = 3+8 = 11, and:sod(456) = 4+5+6 = 15
Sod(D)=7
This is called the digital root of A. Four iterations of Sod will bring a number the size of A down to its digital root.
A has ceil( 2023log2023 ) = 6689 digits which are pretty much evenly distributed. 4.5*6689 = 30100.5 Which is a good approximation for B.
Worst case: suppose B=39999 then C=Sod(B)=39
Then D=Sod(C)=14 and Sod(D) is a single digits.
Sod(2023)=7
Sod(7^2)=13, Sod(13)=4
Sod(4*7)=10, Sod(10)=1
So there is a cycle of length 3.
Since 2023 is 1 mod 3,
The digital root of 2023^2023 is the same as 2023.
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Posted by Jer
on 2022-02-22 13:15:09 |
No Subject
