OEIS A000286: Representations of integers as 2x^2 + 5y^2 up to 2^n

We explore A000286, the count of positive integers ≤ 2^n that can be expressed in the quadratic form 2x^2 + 5y^2. Trace its history (formerly known as n3251 and n312), its appearances in Sloan’s Handbook (1973) and the Encyclopedia of Integer Sequences (1995), and its role in density questions related to Landau’s theorem through Shanks and Schmid. This episode uses a concrete quadratic-form example to illustrate how the OEIS curates patterns, history, and connections across number theory, inviting you to think about distribution and structure in your own studies.

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