In general, for even bases, all [[even and odd numbers|odd]] numbers below the base number are self numbers, since any number below such an odd number would have to also be a 1-digit number which when added to its digit would result in an even number.
The set of self numbers in a given base ''q'' is infinite and has a positive [[asymptotic density]]: when ''q'' is odd, this density is 1/2 [REF].