For a definition, see the wikipedia page: http://en.wikipedia.org/wiki/Strictly_non-palindromic_number
So according to the wikipedia page, under properties, all strictly non-palindromic numbers with three exceptions are primes.
So I have some questions about these numbers. First, what is their relative density in the primes? Does the sum of their reciprocals converge? If not, then do they contain arbitrarily long arithmetic progressions? Are they known to be an additive basis of any order?