Uncanny subsequence selections that generate normal numbers
Joseph Vandehey

TL;DR
This paper explores special subsequences of normal numbers, demonstrating new constructions that preserve normality and showing that removing certain digits from a normal number yields another normal number in a different base.
Contribution
It introduces novel methods for selecting subsequences of normal numbers and proves that digit removal can produce normal numbers in lower bases.
Findings
Arithmetic progression subsequences preserve normality.
Recursively defined subsequences can produce normal numbers.
Removing all (b-1) digits from a normal number yields a normal number in base (b-1).
Abstract
Given a real number that is normal to base , we examine increasing sequences so that the number are normal to base . Classically it is known that if the form an arithmetic progression then this will work. We give several more constructions, including that are recursively defined based on the digits . Of particular interest, we show that if a number is normal to base , then removing all the digits from its expansion which equal leaves a base- expansion that is normal to base .
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