Given a set of integers with no three in arithmetic progression, we construct a Stanley sequence by adding integers greedily so that no arithmetic progression is formed. This paper offers two main contributions to the theory of Stanley sequences. First, we characterize well-structured Stanley sequences as solutions to constraints in modular arithmetic, defining the modular Stanley sequences. Se...

We show that the twisted second moments of the Riemann zeta function averaged over the arithmetic progression 12 + i(an + b) with a > 0, b real, exhibits a remarkable correspondance with the analogous continuous average and derive several consequences. For example, motivated by the linear independence conjecture, we show at least one third of the elements in the arithmetic progression an + b ar...

In many data structure settings, it has been shown that using “double hashing” in place of standard hashing, by which we mean choosing multiple hash values according to an arithmetic progression instead of choosing each hash value independently, has asymptotically negligible difference in performance. We attempt to extend these ideas beyond data structure settings by considering how threshold a...

We present a simple algorithm which for an explicitly given input string pat (a pattern) and a standard Sturmian word x described by the recurrences of size n computes, in time O(|pat|+n), the set of all occurrences of pat in x as a single arithmetic progression (modulo the length of x). The algorithm can be extended to the casewhen some letters of the pattern are replaced by a don’t care symbo...