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ON A PROBLEM ON NORMAL NUMBERS RAISED BY IGOR SHPARLINSKI
Published online by Cambridge University Press: 16 June 2011
Abstract
Given an integer d≥2, a d-normal number, or simply a normal number, is an irrational number whosed-ary expansion is such that any preassigned sequence, of length k≥1, taken within this expansion occurs at the expected limiting frequency, namely 1/dk. Answering questions raised by Igor Shparlinski, we show that 0.P(2)P(3)P(4)…P(n)… and 0.P(2+1)P(3+1)P(5+1)…P(p+1)…, where P(n) stands for the largest prime factor of n, are both normal numbers.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 84 , Issue 2 , October 2011 , pp. 337 - 349
- Copyright
- Copyright © Australian Mathematical Publishing Association Inc. 2011
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