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