# Floor Function and Narcissistic Numbers with Division

Narcissistic numbers are famous in literature. There are very few narcissistic numbers with division. In this work we brought some narcissistic number with division in terms of floor function. Below are some examples and link for download the work. Link for download: Paper

# Narcissistic-Type Selfie Numbers with Division

This work brings extensions of narcissistic numbers in different situations. Extensions are made for positive and negative coefficients, fixed and flexible powers. The idea is extended for narcissistic numbers with division. Here also different situations are considered, such as, positive and negative coefficients, fixed and flexible powers. Comparison with previous known numbers are also given. … Continue reading Narcissistic-Type Selfie Numbers with Division

# Patterns in Semi-Selfie Numbers

Author studied many ways of writing selfie numbers, sometimes known by wild narcissistic numbers. There are numbers very much near to selfie-number, but are not complete selfie numbers. Let us write these types of numbers, as semi-selfie numbers, where numbers are written in terms of expressions with positive, and negative signs having same digits on both … Continue reading Patterns in Semi-Selfie Numbers

# Fibonacci Sequence and Running Expressions with Equalities

In previous work ( Part I   and Part II), running qualities are written in terms of 1 to 9 and 9 to 1 or 9 to 0 separated by single or double equality signs. Each digits is used with basic operations, along with factorial and square-root. These types of equalities, we called as running expressions. … Continue reading Fibonacci Sequence and Running Expressions with Equalities

# 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

# Number Patterns: Single Letter Representations

This work brings representations of palindromic and number patterns in terms of single letter ”a”. Some examples of prime number patterns are also considered. Different classifications of palindromic patterns are considered, such as, palindromic  decompositions, double symmetric patterns, number pattern decompositions, etc. Numbers patterns with power are also studied. Below are some examples and links … Continue reading Number Patterns: Single Letter Representations

# Pythagorean Triples and Perfect Square Sum Magic Squares

This work brings the idea how we can achieve prefect square sum magic squares using primitive and non primitive Pythagorean triples . By perfect square sum magic square, we understand that the total sum of entries of a magic square is a perfect square. The work is divided in two parts, one on primitive triples and another on non primitive … Continue reading Pythagorean Triples and Perfect Square Sum Magic Squares

# 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

# 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