This paper brings natural numbers from 40001 to 60000 written in ascending and
descending orders of 1 to 9. The numbers are obtained by using basic operations, and …

This paper brings natural numbers from 80001 to 10000 written in ascending and
descending orders of 1 to 9. The numbers are obtained by using basic operations, and …

This paper brings natural numbers from 60001 to 80000 written in ascending and
descending orders of 1 to 9. The numbers are obtained by using basic operations, and …

Problems related to the expansions of real numbers in non-integer bases have been
systematically studied since the late 1950's, starting with the seminal works by Rényi [16] …

This work brings representations of natural numbers in three different ways. One is based on
power of same digits used in bases with permutations. The other two are based on …

Let {f,};" be a given sequence of positive integers and consider two fixed sequences,{k;};'and
{md;'of nonnegative integers. Here the terms of the sequence {f,} are to play the role of a …

This paper brings natural numbers from 20001 to 40000 written in ascending and
descending orders of 1 to 9. The numbers are obtained by using basic operations, and …

Throughout this paper,⌊ x⌋ denotes the greatest integer less than or equal to x and⌈ x⌉
denotes the smallest integer greater than or equal to x. Let b⩾ 2 be an integer. For a real …

Expansions in non-integer bases Page 1 Expansions in non-integer bases V. Komornik
University of Strasbourg Erdos 100, Budapest July 5, 2013 V. Komornik (University of …

G untzer and Paul introduced a number system with base 2 and digits 1; 0; 1 which is
characterized by separating nonzero digits by at least one zero. We nd an explicit formula …