OEIS A000229: The smallest moduli where 2 is the least quadratic non-residue

In this episode we dive into A000229, the sequence of the smallest moduli n for which 2 is the least quadratic non-residue. We start with quick reminders of quadratic residues and non-residues, the Legendre symbol, and how residues interact when you move to composite moduli via the Chinese remainder theorem. We unpack what it means for 2 to be the least non-residue and why this simple condition ties together primes, modular arithmetic, and residue classes. The discussion then connects to related ideas—testing non-residues, related OEIS sequences, and the role of quadratic reciprocity—before turning to what is known about how large the first non-residue can be, both unconditionally and under hypotheses like ERH. We also outline practical ways to compute terms and point you to resources in OEIS and the literature for deeper exploration.

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