The simple-normality conjecture for the Fibonacci concatenation
The simple-normality conjecture for the Fibonacci concatenation
The Fibonacci concatenation is the infinite sequence obtained by concatenating the Fibonacci numbers. A sequence is simply normal in base if each digit occurs with limiting frequency .
Simple-normality conjecture. The Fibonacci concatenation is simply normal in every base.
The source proposes this as the route to proving absolute normality: simple normality in every base implies simple normality in every power of every base, after which the cited lemma would yield normality in every base. The conjecture remains open.
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Sources & referencesView supporting material
Primary source
Brennan Benfield and Michelle Manes, “The Fibonacci Sequence is Normal Base 10”, arXiv:2202.08986 (2022).
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