Shuo Li

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math.NT2024

On the Partial Sum of Subword-Counting Sequences

Pranjal Jain, Shuo Li

Let $w$ be a finite word over the alphabet ${0, 1}$ . For any natural number $n$ , let $s_{w} (n)$ denote the number of occurrence of $w$ in the binary expansion of $n$ as a scattered…

math.NT2024

The characteristic sequence of the integers that are the sum of two squares is not morphic

Shuo Li

Let $(s_{2} (n))_{n \in N}$ be a $0, 1$ -sequence such that, for any natural number $n$ , $s_{2} (n) = 1$ if and only if $n$ is a sum of two squares. In a recent article, Tahay prov…