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 […]
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 […]
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 […]
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 […]
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 […]
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 […]
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 […]
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, […]
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. […]
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 […]
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 […]
Palindromic Prime Numbers With 1808 – Today 18.08
Embedded Palprimes with Today Date 8.18 (American Style)
Embedded Palprimes with Today Date: 18.8
Pythagorean Day – 15.8.17
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 […]
