References: Inder J. Taneja, Single Digit Representations of Natural Numbers, Feb. 1015, pp.1-55, http://arxiv.org/abs/1502.03501. Site link: Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000. Inder J. Taneja, Single Digit Representations of Natural Numbers From 1 to 5000, Zenodo, January 14, 2019, http://doi.org/10.5281/zenodo.2538893 Inder J. Taneja, Single Digit Representations of Natural Numbers From 5001 to 10000, Zenodo, January 14, 2019, http://doi.org/10.5281/zenodo.2538897 Inder … Continue reading 11th to 14th Days of Year: 11.01.23 to 14.01.23 – Single Digits Representations and Single Letter Patterns

# Author: Inder J. Taneja

# 23 and 2023 in Numbers and Patterns

This work brings representations of 2023 in different ways. These representations are of crazy-type, running numbers, single digit, single letter, Triangular, Fibonacci, palindromic-type, prime numbers, embedded, repeated digits, colored patterns, magic squares, patterned designs, etc. This year the number 23 is a prime number. Let’s call it prime year. Below is a link of work for download:Inder J. … Continue reading 23 and 2023 in Numbers and Patterns

# Weekly Block of Magic Squares: 1st Block – Different Styles Magic Squares of Orders 6 and 8

Magic Squares of Order 6 There are three magic squares of order 6 given above. The first one is traditional. The second one is bordered and third one is based on bordered magic rectangle of order 4x6. Magic Squares of Order 8 There are 6 magic squares of order 8. The first one is pan … Continue reading Weekly Block of Magic Squares: 1st Block – Different Styles Magic Squares of Orders 6 and 8

# 1st to 10th Days of Year: 01.01.23 to 10.01.23 – Crazy and Single Letter Representations

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ nder J. Taneja, Crazy Representations of Natural Numbers – The 10958 Problem nder J. Taneja, Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterns in Single Letter Representations of Natural Numbers

# 355th to 365th Days of Year: 21.12.22 to 31.12.22 – Crazy and Selfie Representations

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Fibonacci Sequence and Selfie Numbers, Zenodo, February 19, 2019, pp. 1-233, https://doi.org/10.5281/zenodo.2572044. Inder J. Taneja, Triangular-Type Selfie Numbers, … Continue reading 355th to 365th Days of Year: 21.12.22 to 31.12.22 – Crazy and Selfie Representations

# 345th to 354th Days of Year: 11.12.22 to 20.11.22 – Crazy and Power-Plus Representations

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 345th to 354th Days of Year: 11.12.22 to 20.11.22 – Crazy and Power-Plus Representations

# Even Order Figured Magic Squares: A Systematic Procedure

For the first time we are introducing a new idea of magic squares by figures. This work brings magic squares of even orders from 6 to 40. From order 14 onwards, construction idea is explained. It is based on external borders made by cornered magic squares of orders 4, 6, 8, etc. and in middle … Continue reading Even Order Figured Magic Squares: A Systematic Procedure

# 335th to 344th Days of Year: 01.12.22 to 10.11.22 – Crazy Representations Pythagorean Triples Patterns

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 335th to 344th Days of Year: 01.12.22 to 10.11.22 – Crazy Representations Pythagorean Triples Patterns

# Even Order Magic Squares Using Bordered Magic Rectangles

Below are the links of the work as well as sites for the even order magic squares of orders 6, 8, 10, 12, 14, 16, 18 and 20. Inder J. Taneja, Different Styles of Magic Squares of Orders 6, 8, 10 and 12 Using Bordered Magic Rectangles, Zenodo, November 14, 2022, pp. 1-26, https://doi.org/10.5281/zenodo.7319985. Site … Continue reading Even Order Magic Squares Using Bordered Magic Rectangles

# 320th to 327th Days of Year: 16.11.22 to 23.11.22 – Crazy Representations and Pythagorean Triples Patterns

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 320th to 327th Days of Year: 16.11.22 to 23.11.22 – Crazy Representations and Pythagorean Triples Patterns

# 313th to 319th Days of Year: 09.11.22 to 15.11.22 – Crazy and Power-Plus Equality Representations

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 313th to 319th Days of Year: 09.11.22 to 15.11.22 – Crazy and Power-Plus Equality Representations

# 306th to 313th Days of Year: 01.11.22 to 08.10.22 – Crazy and Patterned Selfie Fractions Representations

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 306th to 313th Days of Year: 01.11.22 to 08.10.22 – Crazy and Patterned Selfie Fractions Representations

# 299th to 305th Days of Year: 25.10.22 to 31.10.22 – Crazy, Power-Plus Equality and Semi-Selfie Representations

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 299th to 305th Days of Year: 25.10.22 to 31.10.22 – Crazy, Power-Plus Equality and Semi-Selfie Representations

# 291st to 298th Days of Year: 17.10.22 to 24.10.22 – Crazy, Selfie-Fraction Pattern and Semi-Selfie Representations

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 291st to 298th Days of Year: 17.10.22 to 24.10.22 – Crazy, Selfie-Fraction Pattern and Semi-Selfie Representations

# 283rd to 290th Days of Year: 09.10.22 to 16.10.22 – Crazy, Selfie-Fractions Patterns and Power-Plus Equality Representations

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 283rd to 290th Days of Year: 09.10.22 to 16.10.22 – Crazy, Selfie-Fractions Patterns and Power-Plus Equality Representations

# 275th to 282nd Days of Year: 01.10.22 to 08.10.22 – Crazy and Power-Plus Equality Representations

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 275th to 282nd Days of Year: 01.10.22 to 08.10.22 – Crazy and Power-Plus Equality Representations

# 267th to 274th Days of Year: 24.09.22 to 30.09.22 – Crazy and Power-Plus Equality Representations

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 267th to 274th Days of Year: 24.09.22 to 30.09.22 – Crazy and Power-Plus Equality Representations

# Different Styles of Magic Squares of Orders 8 and 10 Using Bordered Magic Rectangles and the Formula (a+b)^2

For the first time in this work, two new concepts in construction of magic square are considered: Using small blocks of magic or bordered magic rectangles. It is not always possible to write bordered magic rectangles for the non-sequential entries. In this case, the simple magic rectangles are considered. Using algebraic formula (a+b)2. The whole work contains magic squares of even … Continue reading Different Styles of Magic Squares of Orders 8 and 10 Using Bordered Magic Rectangles and the Formula (a+b)^2

# 259th to 266th Days of Year: 16.09.22 to 23.09.22 – Crazy Representations and Patterned Selfie Fractions

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 259th to 266th Days of Year: 16.09.22 to 23.09.22 – Crazy Representations and Patterned Selfie Fractions

# 251st to 258th Days of Year: 08.09.22 to 15.09.22 – Crazy and Power-Plus Equality Representations

References: Inder J. Taneja, Single Digits Representations of Numbers from 1 to 20000, https://inderjtaneja.com/2019/01/01/single-letter-representations-of-numbers-from-1-to-20000/ Crazy Representations of Natural Numbers – The 10958 Problem Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 Inder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096 Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July … Continue reading 251st to 258th Days of Year: 08.09.22 to 15.09.22 – Crazy and Power-Plus Equality Representations