Sum of digits of 2^n equals n

[Hans Havermann]

Tanya Khovanova wrote:

> I found two numbers n such that sum of digits of 2^n is equal to n:  
> 5 and 70.
> I can't find the corresponding sequence.

Because the sequence (likely) only has those two members.

Consider this related sequence: {1, 2, 4, 6, 8, 139, 309, 390, 819,  
2868, 6751, 8045, 9414, 15008, 15375, 56839, ...}

Each n provides a value of (sum-of-digits of 5^n)/n that is closer to  
pi than the previous value. I'm guessing there aren't many more  
terms. ;)
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