OEIS A000074: Odd numbers ≤ 2^n expressible as the sum of two squares

A concise exploration of A000074: the number of odd integers up to 2^n that can be written as a sum of two squares. We unpack Fermat's theorem on sums of two squares, its connection to primes congruent to 1 mod 4, and how A000074 relates to related sequences like A00050 and A00007. We also touch on computational approaches, efficiency considerations, and the surprising links to cryptography that reveal the deeper structure behind this deceptively simple sequence.

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