Perfect digit-to-digit invariant
1 is PDDI in any base. Apart from 1 there is only one other PDDI in the decimal system, 3435. It is important to note that 0 and 438579088 (sequence A046253 in OEIS), are PDDIs under the convention that 00 = 0, but this is not standard usage.
More generally, there are finitely many PDDIs in any base.