8 citations · 48 across the 76 of their papers we have counts for
8 papers · 1 filter
Generalizing the Wythoff Array and other Fibonacci Facts to Tribonacci Numbers
Eric Chen, Adam Ge, Andrew Kalashnikov +8
In this paper, we generalize a lot of facts from John Conway and Alex Ryba's paper, \textit{The extra Fibonacci series and the Empire State Building}, where we replace the Fibonacc…
Base 3/2 and Greedily Partitioned Sequences
Tanya Khovanova, Kevin Wu
We delve into the connection between base and the greedy partition of non-negative integers into 3-free sequences. Specifically, we find a fractal structure on string…
Variants of Base 3 over 2
Matvey Borodin, Hannah Han, Kaylee Ji +8
We discuss two different systems of number representations that both can be called 'base 3/2'. We explain how they are connected. Unlike classical fractional extension, these two s…
On Base 3/2 and its Sequences
Ben Chen, Richard Chen, Joshua Guo +8
We discuss properties of integers in base 3/2. We also introduce many new sequences related to base 3/2. Some sequences discuss patterns related to integers in base 3/2. Other sequ…
Weighted Mediants and Fractals
Dhroova Aiylam, Tanya Khovanova
In this paper we study a natural generalization of the Stern-Brocot sequences which comes from the introduction of weighted mediants. We focus our attention on the case , in…
Stern-Brocot Trees from Weighted Mediants
Dhroova Aiylam, Tanya Khovanova
In this paper we discuss a natural generalization of the Stern Brocot tree which comes from the introduction of weighted mediants. We focus our attention on the case , in wh…
Free Fibonacci Sequences
Brandon Avila, Tanya Khovanova
This paper describes a class of sequences that are in many ways similar to Fibonacci sequences: given n, sum the previous two terms and divide them by the largest possible power of…
Conway's subprime Fibonacci sequences
Richard K. Guy, Tanya Khovanova, Julian Salazar
It's the age-old recurrence with a twist: sum the last two terms and if the result is composite, divide by its smallest prime divisor to get the next term (e.g., 0, 1, 1, 2, 3, 5,…