Explicit Formulas for Concatenations of Terms of An Arithmetic Progression

We construct explicit formulas for sequences of general terms formed by concatenations of the first n + 1 terms of an arithmetic progression in a natural number base. We highlight the non-holonomic character of these sequences and present our implementation for the sequences A007908 and A000422 on https://oeis.org. The code is available at https://github.com/T3gu1a/Concatenations. These formulas are useful for efficient computations of asymptotic terms in these sequences. In the case of A007908, the formula may help investigating the long-standing search of primes among its terms.