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math.NT2026
Gosper's and Ramanujan's infinite products and generalizations
Jean-Paul Allouche, John M. Campbell, Simon R. Holcombe +2
Gosper introduced many remarkable formulas involving infinite products. One such formula provides an evaluation of the product $$\prod_{n \geq 1} \frac{1}{e}\left(\frac{1}{3n} + 1\…
math.NT2026
Meta-automatic Sequences
John M. Campbell, Benoit Cloitre
Nested (or meta-Fibonacci) recurrences, such as the recurrence used to define Hofstadter's Q-sequence, along with the digit-based recurrences that underlie automatic sequences are…
math.NT2024
A binary version of the Mahler-Popken complexity function
John M. Campbell
The (Mahler-Popken) complexity of a natural number is the smallest number of ones that can be used via combinations of multiplication and addition to express , wit…