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

## Single Letter Representations Of Natural Numbers

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

## Flexible Power Representations: Unequal String Lengths

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

## Crazy Representations of Natural Numbers

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

## Running Expressions: Increasing and Decreasing Orders

Running expressions are understood as expressions written in terms of 1 to 9 and 9 to 1 or 9 to 0 separated by one or more equality signs. Each digit appears once with basic operations, along with factorial and square-root. The work is written in increasing and decreasing order of digits, i.e., from 1 to … Continue reading Running Expressions: Increasing and Decreasing Orders

## Crazy Representations of Natural Numbers, Selfie Numbers, Fibonacci Sequence, and Selfie Fractions

This summary brings author's work on numbers. The study is made in different ways. Specially, towards, Crazy Representations of Natural Numbers, Running Expressions, Selfie Numbers, etc. Natural numbers are represented in different situations, such as, writing in terms of 1 to 9 or reverse, flexible power of same digits as bases, single digit, single letter, … Continue reading Crazy Representations of Natural Numbers, Selfie Numbers, Fibonacci Sequence, and Selfie Fractions