Base 3/2

Simon is simply mesmerized by the founder of the Global Math Project James Tanton. He has watched countless tutorials by Tanton and frequents Tanton’s Exploding Dots website that features a revolutionary arithmetic method akin to the ancient abacus but using different number bases.

Base 1.5 (or base 3/2 or “base three halves”) produces a very weird sequence. The sequence consists of the first numbers with n digits in base 3/2:

3, 6, 9, 15, 24, 36, 54, 81, 123, 186, 279, 420, 630, …

We know a formula but it’s not explicit, it depends on the previous number.

number 12 laid out in base 3/2

Simon went on to look for the sequence in the Online Encyclopedia of Integer Sequences and, quite unexpectedly, it was there! And Simon even found a research paper devoted to the sequence, titled “On Base 3/2 and its Sequences” on arxiv.org and that paper actually referred to James Tanton, which blew Simon’s mind. Here come a few excerpts from the paper:

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