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A finite counterexample for strict consecutive totient patterns

Alexander

Palomar Registrypalomar/PALOMAR-2026-10-15-000006Oct 15, 2026math.NTscore 0

Formalizes the finite counterexample at cutoff 826 from Proposition 1.2 of Przemek Chojecki's Consecutive Totient Patterns. With ranks assigned to positions and an inclusive cutoff, every strict length-three permutation occurs, no increasing length-four block occurs, and a decreasing length-four block does occur. Hence the largest universal length is three and decreasing is not always absent at the first non-universal length. This is a partial negative result for a specified reading of Erdos Problem 415; no novelty, asymptotic result or natural weak-order frequency result is claimed.

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