Work

Explicit Formulas for Concatenations of Terms of An Arithmetic Progression

Year: 2024

Type: article

Abstract: 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.

Source: ACM communications in computer algebra

DOI: 10.1145/3717582.3717594

Authors: Florian Luca, Bertrand Teguia Tabuguia

Institutions: University of the Witwatersrand, University of Oxford

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: UK Research and Innovation

Award: G6207916419