Nathan Fox

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math.NT2024

Elated Numbers

N. Bradley Fox, Nathan H. Fox, Helen G. Grundman +3

For a base $b \geq 2$ , the $b$ -elated function, $E_{2, b}$ , maps a positive integer written in base $b$ to the product of its leading digit and the sum of the squares of its digits.…

math.NT2024

The Behavior of a Three-Term Hofstadter-Like Recurrence with Linear Initial Conditions

Nathan Fox

In this paper, we study the three-term nested recurrence relation $B (n) = B (n - B (n - 1)) + B (n - B (n - 2)) + B (n - B (n - 3))$ subject to initial conditions where the first $N$ terms are the integer…