Journal of Integer Sequences, Vol. 23 (2020), Article 20.2.7

Variants of Base 3 Over 2


Matvey Borodin, Hannah Han, Kaylee Ji, Alexander Peng, David Sun,
Isabel Tu, Jason Yang, William Yang, Kevin Zhang, and Kevin Zhao
PRIMES STEP
Department of Mathematics
MIT
77 Massachusetts Avenue
Cambridge, MA 02139
USA

Tanya Khovanova
Department of Mathematics
MIT
77 Massachusetts Avenue
Cambridge, MA 02139
USA

Abstract:

We conjecture that the sequence of even non-negative integers represented in base 3/2 and then evaluated in base 3 is the same as the sequence of first terms of the infinite number of sequences that represent a greedy partition of non-negative integers into 3-free sequences. We also discuss some new sequences related to base 3/2.

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(Concerned with sequences A005836 A024629 A244040 A256785 A261691 A265316 A320035 A320272 A320273 A320274 A322298 A323398 A323418 A323419.)

Received March 27 2019; revised version received April 3 2019; January 27 2020; February 16 2020; February 18 2020. Published in Journal of Integer Sequences, February 20 2020.

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