Add to ORKGGiven an integer q>1, a q-normal number is an irrational number r such that any preassigned sequence of k digits occurs in the q-ary expansion of r at the expected frequency, namely 1/q^k. In a recent paper, we constructed a large family of normal numbers, showing in particular that the numbers 0.P(2)P(3)P(4)... 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 normal numbers, thereby answering in the affirmative a question raised by Igor Shparlinski. Here, we show that, given any fixed integer k>1, the numbers 0.P_k(2)P_k(3)P_k(4)... and 0.P_k(2+1)P_k(3+1)P_k(5+1)...P_k(p+1)..., where P_k(n) stands for the k-th largest prime factor of n, are normal numbers. Much more general results are also obt...
Let s be an integer greater than or equal to 2. A real number is simply normal to base s if in its b...
For an integer b ≥ 2 a real number α is b -normal if, for all m > 0, every m-long string of digits i...
summary:Let $Q=(q_n)_{n=1}^\infty $ be a sequence of bases with $q_i\ge 2$. In the case when the $q_...
Given an integer q>1, a q-normal number is an irrational number r such that any preassigned sequence...
Given an integer $d\ge 2$, a $d$-{\it normal number}, or simply a {\it normal number}, is an irratio...
International audienceIn the present paper we construct normal numbers in base $q$ by concatenating...
A number is normal to the base r if, in its expansion to that base, all possible digit strings of le...
We use probabilistic methods, along with other techniques, to address three topics in number theory ...
It is well known that almost all real numbers (in the sense of Lebesgue measure) are normal to base ...
AbstractWe show that the number generated by the q-ary integer part of an entire function of logarit...
We call a family of primes P normal if it contains no two primes p; q such that p divides q \Gamma ...
Abstract The purpose of this paper is to introduce a new pattern in Primes numbers, to eliminate the...
It is widely believed that several fundamental mathematical constants, like pi, e, log 2 and so on, ...
In this paper, we study the linear independence between the distribution of the number of prime fact...
Abstract. Let g ≥ 2. A real number is said to be g-normal if its base g expansion contains every fin...
Let s be an integer greater than or equal to 2. A real number is simply normal to base s if in its b...
For an integer b ≥ 2 a real number α is b -normal if, for all m > 0, every m-long string of digits i...
summary:Let $Q=(q_n)_{n=1}^\infty $ be a sequence of bases with $q_i\ge 2$. In the case when the $q_...
Given an integer q>1, a q-normal number is an irrational number r such that any preassigned sequence...
Given an integer $d\ge 2$, a $d$-{\it normal number}, or simply a {\it normal number}, is an irratio...
International audienceIn the present paper we construct normal numbers in base $q$ by concatenating...
A number is normal to the base r if, in its expansion to that base, all possible digit strings of le...
We use probabilistic methods, along with other techniques, to address three topics in number theory ...
It is well known that almost all real numbers (in the sense of Lebesgue measure) are normal to base ...
AbstractWe show that the number generated by the q-ary integer part of an entire function of logarit...
We call a family of primes P normal if it contains no two primes p; q such that p divides q \Gamma ...
Abstract The purpose of this paper is to introduce a new pattern in Primes numbers, to eliminate the...
It is widely believed that several fundamental mathematical constants, like pi, e, log 2 and so on, ...
In this paper, we study the linear independence between the distribution of the number of prime fact...
Abstract. Let g ≥ 2. A real number is said to be g-normal if its base g expansion contains every fin...
Let s be an integer greater than or equal to 2. A real number is simply normal to base s if in its b...
For an integer b ≥ 2 a real number α is b -normal if, for all m > 0, every m-long string of digits i...
summary:Let $Q=(q_n)_{n=1}^\infty $ be a sequence of bases with $q_i\ge 2$. In the case when the $q_...