Allan Wechsler <acwacw@gmail.com> wrote:

Andy Latto <andy.latto@pobox.com> wrote:

...

I find the pattern in the first row of your table very interesting.

Thank you.

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Is there any intuitive reason that pandigital numbers in odd bases only have very small powers of two as divisors?

I'm making a very big free-associative leap, but this topic seems vaguely related to something I've thought of as "reverse long division". I'd like to know whether it's been studied; I think the problem under discussion is in the same conceptual area. ....

Interesting. I had not thought of that. However, there is a different reason why every other odd-numbered base has 0 for its highest power of 2. I finished calculating the 14th term, i.e. the highest power of 2 that divides any 14-digit base-14 pandigital number. It's 36. This took more than a full day. Calculating it for 15 would take two weeks, and for 16 nearly a year. But I didn't need to, as I solved those two powers in my head. For 15 it's 0, and for 16 it's 7. And there are more than 87 billion solutions for 7. (I won't list them all.) Can you see how I was able to solve those in my head? Warning: My next post to this list should not be taken seriously. It will contain some physics and chemistry, and perhaps some humor, but relatively little math. It may be offensive to Republicans and Democrats.