OEIS A000277: Predictable jumps behind a floor-root formula

Dive into A000277, an easy-sequence with a compact formula involving a square root and floor. Despite the appearance of complexity, the terms march forward in a simple rhythm: alternating +1 and +3 jumps driven by how floor(sqrt(4n+5)) behaves as n increases. We'll show how the floor term stays constant over stretches and then jumps, tweaking the net increment, and why OEIS labels this 'easy'. We'll explore generation with Mathematica and PARI/GP snippets, the offset, and cross-references to related sequences, and discuss what deeper connections might be hiding in the entry.

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