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Power of 2 (Posted on 2016-05-27) Difficulty: 4 of 5
Find integers N for which the sum of the digits in 2N equals N.

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

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Some Thoughts What I can find | Comment 1 of 6
By checking digital roots
N 2^N
0  1
1  2
2  4
3  8
4  7
5  5
6  1
7  2
8  4
9  8
10 7
11 5
and noting the cycle in the 2^N column it is clear that most numbers don't have a chance.  
In fact only if N is of the form 18a+5 will the digital roots of N and 2^5 be the same (5).
I could only check 5, 23, 41 on my calculator and only N=5 works.

It's possible, but unlikely there are other solutions, but the number of digits of 2^N grows as log(2) and the sum of digits grows as 4.5log(2)=1.35 it would be surprising to see another solution.

  Posted by Jer on 2016-05-27 11:40:18
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