# Fixed and Flexible Powers Narcissistic Numbers with Division

This works brings fix and flexible powers narcissistic numbers with divison extending the original idea of narcissistic numbers. This is a revised and enlarged version of author’s previous work. The general case without division is given in another work. In this work we have considered following possibilities: Fixed Power: Positive Coefficients; Fixed Power: Positive and Negative Coefficients; Flexible … Continue reading Fixed and Flexible Powers Narcissistic Numbers with Division

# Flexible Powers Narcissistic-Type Numbers

This works brings flexible powers narcissistic numbers with positive, and positive-negative coefficients extending the original idea of narcissistic numbers. This is a revised and enlarged version of author's previous work. The extension of this work with division is given in another page. Below are examples and a link for download. Inder J. Taneja,  Flexible Powers … Continue reading Flexible Powers Narcissistic-Type Numbers

# Binomial Coefficient Type Selfie Numbers: Reverse Order of Digits

The numbers represented by its own digits by use of operations, such as, basic operations with factorial, square-root, etc. are known as “selfie numbers“.  This work is  revised and enlarged version of author’s previous work on Selfie numbers with binomial coefficients. The previous work is only up to five digits. This work is extended to six digits. There … Continue reading Binomial Coefficient Type Selfie Numbers: Reverse Order of Digits

# Binomial Coefficient Type Selfie Numbers: Digit’s Order

The numbers represented by its own digits by use of operations, such as, basic operations with factorial, square-root, etc. are known as "selfie numbers".  This work is  revised and enlarged version of author's previous work on Selfie numbers with binomial coefficients. The previous work is only up to five digits. This work is extended to … Continue reading Binomial Coefficient Type Selfie Numbers: Digit’s Order

# Selfie Numbers and Binomial Coefficients

During past years, author studied different types of “selfie numbers”, with extra operations as, factorial, square-root, Fibonacci sequence values, etc. This paper brings “selfie numbers” in terms of “binomial coefficients”. This has been done in digit’s order, reverse order of digits and in both ways. The results are limited to five digits. Below are examples examples and link for download the work: Link … Continue reading Selfie Numbers and Binomial Coefficients

# Digit’s Order Selfie Numbers: Factorial and Square-Root

Numbers represented by their own digits by certain operations are considered as selfie numbers. Some times they are called as wild narcissistic numbers. There are many ways of representing selfie numbers. They can be represented in digit's order, reverse order of digits, increasing and/or decreasing order of digits, etc. These can be obtained by use … Continue reading Digit’s Order Selfie Numbers: Factorial and Square-Root

# Concatenation-Type Selfie Numbers With Factorial and Square-Root

Numbers represented by their own digits by certain operations are considered as selfie numbers. Some times they are called as wild narcissistic numbers. There are many ways of representing selfie numbers. They can be represented in digit's order, reverse order of digits, increasing and/or decreasing order of digits, etc. These can be obtained by use … Continue reading Concatenation-Type Selfie Numbers With Factorial and Square-Root

# 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

# 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 … Continue reading Semi-Selfie Numbers

# Factorial-Power Selfie Expressions

This work brings numbers in such a way that both sides of the expressions are with same digits. One side is digits with factorial and another side are with same digits with respective powers. These types of expressions, we call as selfie expressions. Many ways of these types of expressions are studied. For distinct and … Continue reading Factorial-Power Selfie Expressions

# Selfie Numbers and Binomial Coefficients

During past years, author studied different types of "selfie numbers", with extra operations as, factorial, square-root, Fibonacci sequence values, etc. This paper brings "selfie numbers" in terms of "binomial coefficients". This has been done in digit's order, reverse order of digits and in both ways. The results are limited to five digits. See below some examples:   … Continue reading Selfie Numbers and Binomial Coefficients