OEIS A000227: Nearest integer to e and the integer maximizer

Explore A000227, the sequence of integers closest to e, which begins 1, 3, 7, 20, 55, 148 and is indexed from 0. We trace the surprising link to a related discrete maximization problem for the function 6^{k!}, the observation by Stanislav Sikora that the integer argmax aligns with the rounded continuous peak, and the high-precision A000227Test that finds no counterexamples up to n > 24,500. We discuss the heuristic (not a proof) based on peak symmetry, and place this curious coincidence in historical context with notes on indexing and connections to related sequences.

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