OEIS A000015: Prime Powers and Runs

In this episode we dive into OEIS sequence A000015, the smallest prime power greater than or equal to n. We’ll unpack what prime powers are, illustrate how the sequence stays constant for a while before jumping to 4, 8, 9, 11, and so on, and explain why those runs relate to gaps between prime powers—and to bigger prime questions like twin primes. We’ll peek at the formulas and code snippets in the OEIS entry (Maple, Mathematica, PIR, Haskell) and touch on connections to related sequences such as A031218 (as noticed by Colin Linster). Along the way we discuss why prime powers matter in cryptography, computer science, and number theory, and invite you to explore A000015 yourself on OEIS.

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