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In this article, we give a particular recreational application of thesequence A000533 and A261544 in "The On-line Encyclopedia of Integer Sequences"(OEIS). The recreational application provides a direct extension to "TheRepetitious Number" puzzle of Martin Gardner contained in The Second ScientificAmerican Book of Mathematical Puzzles and Diversions published in 1961. We thenprovide a generalization to the repetitious number puzzle and give a relatedpuzzle as an illustrative example. Finally, as a consequence of thegeneralization, we define a family of sequence in which the sequences A000533and A261544 belong.

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