A Computational Study of Base-b Deletable Primes

A prime is deletable in base b if its base-b digits can be removed one at a time, never creating a leading zero, so that every intermediate number is prime, ending at a single-digit prime. We carry out a systematic computation of the counts of n-digit base-b deletable primes for 3 <= b <= 12, contributing many new terms to ten OEIS sequences that had stalled at brute-force depth. The counts grow geometrically, and the per-step growth ratio splits sharply by the parity of b: even bases grow about twice as fast as the odd base just below them. We explain this by factoring the ratio into a mean offspring count and a mean number of deletable parents; the offspring count is governed by b^2/(phi(b) ln b), so the parity dichotomy comes entirely from phi(b). We also prove two elementary obstruction theorems on which single-digit roots a deletable prime can reach, one modulo 2 (all odd bases) and one modulo 3 (bases b = 1 mod 3, generalizing an observation of Andersen for base 10), and we show by explicit counterexamples that the analogue fails for every modulus q >= 5. Finally we record several new integer sequences. All code and verification records are public.