Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I recently saw a conjecture on a blog ( http://blog.tanyakhovanova.com/?p=311 ) which the author refers to as the 86 conjecture. The conjecture claims that all powers of 2 greater than $2^{86}$ have a zero in their base 10 representation.

At first glance this seems like a numerical curiosity, and I wasn't sure that this was an interesting or deep mathematical question. I wanted to ask the community if they knew of any existing work that deals with either this type of question or something similar.

I tried searching for 86 conjecture on Google and didn't get anything useful.

share|improve this question
add comment

1 Answer

up vote 11 down vote accepted

Richard Guy's Unsolved Problems in Number Theory, Problem F24, mentions only that Dan Hoey has verified this conjecture for $2^n$ up to $n = 2,500,000,000$. Guy tends to be fairly complete in his references. Since he doesn't give any others I doubt there's much more out there.

Several other related questions on decimal representations of powers of integers appear in F24 as well, most of which also appear to be open problems. There are some sequences in the On-line Encyclopedia of Integer Sequences mentioned, too; those might be worth chasing down.

share|improve this answer
    
Thanks for the reference. This problem really is in the mathematical wilderness. –  svenkatr Mar 8 '11 at 2:57
3  
The main sequence is A007377. –  Charles Mar 8 '11 at 3:40
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.