Single Digits Representations of Numbers from 1 to 20000

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

Crazy Representations of Natural Numbers – The 10958 Problem

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

Product and Power Type Amicable Numbers

In the history, there are numbers known by Amicable numbers  (see Madachy, 1966, p. 155). There are many different ways of expressing these numbers. Most famous among them is with operation of addition, such as 220 and 284. In this case the summing the divisors of one we get another number. But there are other … Continue reading Product and Power Type Amicable Numbers

Single Digit Representation of Natural Numbers 1 to 10000

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

Double and Triple Sequential Representations of Natural Numbers

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

Pyramidical-Type 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

Flexible Power Representations: Equal String Lengths

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