Counterexamples to a conjecture of Kamenetsky on OEIS A173419

Abstract

Define a(n) as the number corresponding to the shortest computation using only addition, subtraction, or multiplication, as A173419 states on the related OEIS page. In a comment to the sequence, D. Kamenetsky conjectured that a(p) $\ge$ a(p -1) for every prime. We show that the conjecture is false through four counterexamples below 5000 that satisfy the condition a(p)<a(p -1). They are exactly 3359, 3623, 4909, and 4943.