  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.
