Repunit Coordinates for the Erdős Ternary-Digit Problem

Paul Erdős conjectured that the only powers of two whose ternary expansions contain no digit 2 are 1, 4, and 256. Despite extensive computational verification, the conjecture remains open. We reformulate the problem using generalised base-4 repunits. Any admissible exponent is even, say \(n=2s\), an