4 papers · 1 filter
Non-standard Zeckendorf decompositions; or, Tribonacci within Fibonacci
Katie Anders, Madeline L. Dawsey, Joseph Vandehey
We study , the number of ways of writing as a sum or difference of the first Fibonacci numbers. We show that satisfies the Tribonacci-like recurrence $B(0;…
Non-standard quaternary representations and the Fibonacci numbers
Katie Anders, Madeline L. Dawsey, Rajat Gupta +2
Let be the number of hyperquaternary representations of and be the number of balanced quaternary representations of . We show that there is no integer …
Partition-theoretic model of prime distribution
Aidan Botkin, Madeline L. Dawsey, David J. Hemmer +2
We make an application of ideas from partition theory to a problem in multiplicative number theory. We propose a deterministic model of prime number distribution, from first princi…
Representations of integers as quotients of sums of distinct powers of three
Katie Anders, Madeline Locus Dawsey, Bruce Reznick +1
Which integers can be written as a quotient of sums of distinct powers of three? We outline our first steps toward an answer to this question, beginning with a necessary and almost…