# A Recreational Application of Two Integer Sequences and the Generalized Repetitious Number Puzzle

## TL;DR

This paper explores a recreational application of specific integer sequences from OEIS, extending the classic Repetitious Number puzzle and introducing a generalized family of sequences with related puzzles.

## Contribution

It introduces a novel generalization of the Repetitious Number puzzle using two OEIS sequences, expanding the scope of recreational mathematical puzzles.

## Key findings

- Extended the Repetitious Number puzzle with a new generalized framework.
- Defined a family of sequences including A000533 and A261544.
- Provided illustrative examples demonstrating the generalized puzzle.

## Abstract

In this article, we give a particular recreational application of the sequence A000533 and A261544 in "The On-line Encyclopedia of Integer Sequences" (OEIS). The recreational application provides a direct extension to "The Repetitious Number" puzzle of Martin Gardner contained in The Second Scientific American Book of Mathematical Puzzles and Diversions published in 1961. We then provide a generalization to the repetitious number puzzle and give a related puzzle as an illustrative example. Finally, as a consequence of the generalization, we define a family of sequence in which the sequences A000533 and A261544 belong.