https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:12923 b,c = Σ_n≥1 1/(cⁿb^cn), for coprime integers b ≥ 2 and c ≥ 2. These are of interest because, according to previous studies, α_b,c is known to be b-normal, meaning that every m-long string of base-b digits appears in the base-b expansion of the constant with precisely the limiting frequency b^-m. So, for example, the constant α_2,3 = Σn≥1 1/(3ⁿ2³ⁿ) is 2-normal. More recently it was established that α_b,c is not bc-normal, so, for example,α_2,3 is provably not 6-normal. In this paper, we extend these findings by showing that α_b,c is not B-normal, where B = b^pc^q r, for integers b and c as above, p, q, r ≥ 1, neither b nor c divide r, and the condition D=c^q/pr^1/p/b^c-1 < 1 is satisfied. It is not known whether or not this is a complete catalog of bases to which α_b,c is nonnormal. We also show that the sum of two B-nonnormal Stoneham constants as defined above, subject to some restrictions, is B-nonnormal.]]> Wed 11 Apr 2018 10:56:19 AEST ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:15946 0, every m-long string of digits in the base-b expansion of α appears, in the limit, with frequency b^-m. Although almost all reals in [0, 1] are b-normal for every b, it has been rather difficult to exhibit explicit examples. No results whatsoever are known, one way or the other, for the class of “natural” mathematical constants, such as π,e,2√ and log2. In this paper, we summarize some previous normality results for a certain class of explicit reals and then show that a specific member of this class, while provably 2-normal, is provably not 6-normal. We then show that a practical and reasonably effective pseudorandom number generator can be defined based on the binary digits of this constant and conclude by sketching out some directions for further research.]]> Sat 24 Mar 2018 08:23:41 AEDT ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:20656 m. As a consequence of this result, we prove two recent conjectures of Aragón Artacho et al. [‘Walking on real numbers’, Math. Intelligencer 35(1) (2013), 42–60] concerning the base-b expansion of Stoneham numbers.]]> Sat 24 Mar 2018 07:49:58 AEDT ]]>