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.
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: