OEIS A000244: Powers of 3

In this Deep Dive we explore OEIS A000244, the simple-looking sequence 3^n, and uncover why powers of three show up so often across mathematics. We trace how base-3 representations and the concept of radix economy highlight why three is a natural, efficient choice among integer bases, and we glimpse balanced ternary and ternary logic as elegant alternatives for handling sign and state. History and computing context come alive with early ternary machines—the Fowler calculator and the CETON computer—and a discussion of why binary ultimately prevailed. The episode also surveys fractions in base 3, grouping digits into trits, and three-way choices in combinatorics (three options per element, yielding 3^n), plus three-step walks on triangle graphs and related counting problems. In geometry, the total number of faces of a d-dimensional cube is 3^d, linking to broader themes about three-state structures. We touch fractals and self-similar constructions built around thirds, and even a nod to conjectural ideas about three’s role in geometry. If you thought 3^n was just a simple exponent, this episode shows how it threads through number systems, counting, geometry, and the history of computation.

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