In the previous work, we established representations of numbers numbers from 0 to 1000 using only single digit, i.e., in terms of  1, 2, 3, 4, 5, 6, 7, 8 and 9. This is done only using basic operations: addition, subtraction, multiplication, potentiation and division. The same work is extended natural numbers up to 10000.  Below … Continue reading Single Digits Representations of Numbers from 1 to 20000

In 2013-2014, author (click here) wrote natural numbers in increasing and decreasing orders of 1 to 9 using only basic operations. See below some examples: This work has been considered as "Improbable Research". For details see the links: (i)  http://www.improbable.com/2013/02/12/lots-of-numbers-plain-and-almost-simple/; (ii) http://www.improbable.com/2013/06/08/lots-more-numbers-deemed-crazy-sequential/ Also refer Nebus 1, Nebus 2  for more comments. We observe that the … Continue reading Crazy Representations of Natural Numbers – The 10958 Problem

In the previous work, we established representations of numbers numbers from 0 to 1000 using only single digit, i.e., in terms of  1, 2, 3, 4, 5, 6, 7, 8 and 9. This is done only using basic operations: addition, subtraction, multiplication, potentiation and division. The same work is extended natural numbers up to 10000.  Below … Continue reading Single Digit Representation of Natural Numbers 1 to 10000

This work brings representations of natural numbersin two different ways. In both the representations, the same digits, i.e., 3 to 0, 4 to 0, 5 to 0, 6 to 0, 7 to 0, 8 to 0, etc. decreasing order. The work is divided in four papers with links given below. In case of triple reprentations, … Continue reading Double and Triple Sequential Representations of Natural Numbers

This work brings pyramidical-type representations of natural numbers in two different ways. In both the representations same digits are used always ending in 0 such as, 210, 3210, etc.. In one way, we used the based and expoentes of same digits, and in the second way we used, basic operations alongwith factorial and square-root etc. … Continue reading Pyramidical-Type Representations of Natural Numbers

This work brings natural numbers from 0 to 11111 written in terms of 0 to 9 in such a way that both expoents and bases are of same digits, from 0 to 9, but with permutable powers. See below some examples and link for download the complete work. Link for download: 1-50000 1. Equal Length Strings … Continue reading Flexible Power Representations: Equal String Lengths

This is first work if its kind. It brings representations of natural numbers from 0 to 5000 written in terms of single digit "a".  It is in such a way that if we replace a by 1 to 9, it always remains the same. To bring these results only basic operations, such as, addition, subtraction, … Continue reading Single Letter Representations Of Natural Numbers

This paper works with representations of natural numbers from 0 to 11111 written in terms of expressions with additions, subtractions and exponents. Digits used are from 1 to 9 in such a way that for each number, there are same digits in bases and exponents with different permutations. Some numbers can be written in more than one … Continue reading Flexible Power Representations: Unequal String Lengths

Natural numbers from 0 to 11111 are written in terms of 1 to 9 in two different ways. The first one in increasing order of 1 to 9, and the second one in decreasing order. This is done by using the operations of addition, multiplication, subtraction, potentiation, and division. In both the situations there are … Continue reading Crazy Representations of Natural Numbers