Since divisibility by 2 and 5 is such a problem, why not look for memorable numbers in prime base, like base 7 or base 11?
Why do we care about base 10 ? Because we have five digits per appendage ? BFD. Accident of evolution.
What about palindromes in binary ? That's about as close to a mathematical ideal as we could get. Yes?
Let's see. decimal 11 = binary 1011, its palindrome = 1101 = decimal 13, GOLD!
If we allow non-decimal bases, (2^n)-1 works for a lot of memorable values of n (e.g. 2, 3, 5, 7... and 31, per the article), or some less memorable but very long values of n, like 136279841
They're all technically palindromes in base-2.
I can't tell if this is a joke if if you're serious