Numbers with Integer Complexity Close to the Lower Bound I

Abstract

WARNING: OLD DRAFT. Define f(n) to be the integer complexity of n, the smallest number of ones needed to write n using an arbitrary combination of addition and multiplication. John Selfridge showed that f(n) ≥ 3 log3 n for all n. Define d(n) = f(n) − 3 log3 n; in this paper we present a method for classifying all n with d(n) < r for a given r. From this, we… (More)

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