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Algebraic Proof of Completeness of a Positional Numeral System in the Normalized Mersenne Basis
This paper introduces and investigates a non-classical positional numeral system constructed on the normalized Mersenne basis $M_k = (2^k-1)/3$, structurally linking the classical Mersenne sequence (OEIS \textbf{A000225}) with the integer sequence of alternating binary bitmasks (OEIS \textbf{A002450
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