36th to 39th Days of Year: 05.02.23 to 08.02.23 – Single Digits and Semi-Selfie Representations

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 36th to 39th Days of Year: 05.02.23 to 08.02.23 – Single Digits and Semi-Selfie Representations

32nd to 35th Days of Year: 01.02.23 to 04.02.23 – Single Digits and Semi-Selfie Representations

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 32nd to 35th Days of Year: 01.02.23 to 04.02.23 – Single Digits and Semi-Selfie Representations

27th to 31st Days of Year: 27.01.23 to 31.01.23 – Single Digits and Single Letter Representations

References: Single Digits 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, … Continue reading 27th to 31st Days of Year: 27.01.23 to 31.01.23 – Single Digits and Single Letter Representations

25th to 31st Days of Year: 25.01.23 to 31.01.23 – Crazy 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 item Inder J. Taneja, Semi-Selfie Numbers, \textbf{Zenodo}, February 12, 2019, pp. 1-394, https://doi.org/10.5281/zenodo.2562390. Inder J. Taneja, Patterns in Selfie and Semi-Selfie … Continue reading 25th to 31st Days of Year: 25.01.23 to 31.01.23 – Crazy and Semi-Selfie Representations

23rd to 26th Days of Year: 23.01.23 to 26.01.23 – Single Digits and Single Letter Representations

References: Single Digits 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, … Continue reading 23rd to 26th Days of Year: 23.01.23 to 26.01.23 – Single Digits and Single Letter Representations

19th to 22nd Days of Year: 19.01.23 to 22.01.23 – Single Digits and Single Letter Representations

References: Single Digits 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, … Continue reading 19th to 22nd Days of Year: 19.01.23 to 22.01.23 – Single Digits and Single Letter Representations

17th to 24th Days of Year: 17.01.23 to 24.01.23 – Crazy 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 item Inder J. Taneja, Semi-Selfie Numbers, \textbf{Zenodo}, February 12, 2019, pp. 1-394, https://doi.org/10.5281/zenodo.2562390. Inder J. Taneja, Patterns in Selfie and Semi-Selfie … Continue reading 17th to 24th Days of Year: 17.01.23 to 24.01.23 – Crazy and Semi-Selfie Representations

15th to 18th Days of Year: 15.01.23 to 18.01.23 – Single Digits and Single Letter Representations

References: Single Digits 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, … Continue reading 15th to 18th Days of Year: 15.01.23 to 18.01.23 – Single Digits and Single Letter Representations

11th to 16th Days of Year: 11.01.23 to 16.01.23 – Crazy 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 item Inder J. Taneja, Semi-Selfie Numbers, \textbf{Zenodo}, February 12, 2019, pp. 1-394, https://doi.org/10.5281/zenodo.2562390. Inder J. Taneja, Patterns in Selfie and Semi-Selfie … Continue reading 11th to 16th Days of Year: 11.01.23 to 16.01.23 – Crazy and Semi-Selfie Representations

11th to 14th Days of Year: 11.01.23 to 14.01.23 – Single Digits and Single Letter Representations

References: Single Digits 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, … Continue reading 11th to 14th Days of Year: 11.01.23 to 14.01.23 – Single Digits and Single Letter Representations

23rd to 26th Days of Year: 23.01.23 to 26.01.23 – Single Digits and Single Letter Representations

References: Single Digits 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, … Continue reading 23rd to 26th Days of Year: 23.01.23 to 26.01.23 – Single Digits and Single Letter Representations

11th to 14th Days of Year: 11.01.23 to 14.01.23 – Single Digits Representations and Single Letter Patterns

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

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