Thanks for the pointer to OEIS, Hans, and thanks to Neil for enabling it! OK, my most recent estimate of the number of dual palindromes -- assuming the two number bases are in a sense "independent" as I'd expect 2 and 3 to be -- is that the total number is probably *finite*. So, QUESTION: Is the number of dual palindromes to bases 2 and 3 finite? ------ What about to any two different prime number bases? --Dan On 2013-11-21, at 2:44 PM, Dan Asimov wrote:
Here's a question a friend and I have been looking at very casually, with only the partialest results:
Given two bases B and C, what is the asymptotic fraction of positive integers that are palindromes when expressed to each base?
Perhaps to make things simpler, assume that B and C are relatively prime.
Or are each prime.
In fact, just for definiteness, what is the expected number of integers between 1 and N that are palindromes both to base 2 and to base 3 ???
--Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun