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