21st, 22nd and 23rd Days of the Year: 21.01.26, 22.01.26 and 23.01.26 – Recreating Numbers and Patterns

References

1. Crazy Representations

1. Inder J. Taneja, The Crazy Representations and 10958 Problem
   • Crazy Representations of Natural Numbers – The 10958 Problem – Numbers Magic (wordpress.com)
   • Crazy Representations of Natural Numbers – The 10958 Problem – Recreating Numbers and Magic Squares (numbers-magic.com)
2. Inder J. Taneja, Crazy Representations of Natural Numbers Using Factorial: From 20001-100000
   • Crazy Representations of Natural Numbers Using Factorial: From 20001-100000 – Numbers Magic (wordpress.com)
   • Crazy Representations of Natural Numbers Using Factorial: From 20001-100000 – Recreating Numbers and Magic Squares (numbers-magic.com)
3. Inder J. Taneja, Crazy Representations of Natural Numbers Using Factorial: From 100001-200000
   • Crazy Representations of Natural Numbers Using Factorial: From 100001-200000 – Numbers Magic (wordpress.com)
   • Crazy Representations of Natural Numbers Using Factorial: From 100001-200000 – Recreating Numbers and Magic Squares (numbers-magic.com)
4. Inder J. Taneja, Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000
   • Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 – Numbers Magic (wordpress.com)
   • Crazy Representations of Natural Numbers Using Factorial From 200001 to 300000 – Recreating Numbers and Magic Squares (numbers-magic.com)
5. Inder J. Taneja, Representation of Numbers from 1 to 20000 in Terms of Palindromic Digits 1357-9-7531
   • Representation of Numbers from 1 to 20000 in Terms of Palindromic Digits 1357-9-7531 – Numbers Magic (wordpress.com)
   • Representation of Numbers from 1 to 20000 in Terms of Palindromic Digits 1357-9-7531 – Recreating Numbers and Magic Squares (numbers-magic.com)
6. Inder J. Taneja, Representation of Numbers from 1 to 10000 in Terms of Palindromic Digits 2022-2202, 
   • Representation of Numbers from 1 to 10000 in Terms of Palindromic Digits 2022-2202 – Numbers Magic (wordpress.com)
7. Inder J. Taneja, Multiple Choices for Crazy Representations of Natural Numbers
   • Multiple Choices for Crazy Representations of Natural Numbers – Numbers Magic (wordpress.com)
   • Multiple Choices for Crazy Representations of Natural Numbers – Recreating Numbers and Magic Squares (numbers-magic.com)

2. Running Equalitiy Expressions

• Inder J. Taneja, Running Expressions in Increasing and Decreasing Orders of Natural Numbers Separated by Equality Signs, RGMIA Research Report Collection, 18(2015), Article 27, pp.1-54, http://rgmia.org/papers/v18/v18a27.pdf.
• Inder J. Taneja, Running Expressions with Equalities: Increasing and Decreasing Orders – I, RGMIA Research Report Collection, 20(2017), Art. 33, pp.1-57, http://rgmia.org/papers/v20/v20a33.pdf.
• Inder J. Taneja, Running Expressions with Equalities: Increasing and Decreasing Orders – II, RGMIA Research Report Collection, 20(2017), Art. 34, pp.1-87, http://rgmia.org/papers/v20/v20a34.pdf.
• Inder J. Taneja, Fibonacci Sequence and Running Expressions with Equalities – I, RGMIA Research Report Collection, 20(2017), Art. 35, pp. 1-83, http://rgmia.org/papers/v20/v20a35.pdf.
• Inder J. Taneja, Running Expressions with Triangular Numbers – I, Zenodo, December 21, 2018, http://doi.org/10.5281/zenodo.2483327.
• Inder J. Taneja, Crazy Running Equality Expressions with Factorial and Square-Root, Zenodo, December 06, 2021, pp. 1-464, https://doi.org/10.5281/zenodo.5761752.

3. Pattern in Pythagorean Triples

1. Inder J. Taneja, Patterns in Pythagorean Triples Using Single and Double Variable Procedures, Zenodo, January 19, 2019, pp. 1-134, http://doi.org/10.5281/zenodo.2544519.
2. Inder J. Taneja, Multiple-Type Patterns and Pythagorean Triples, Zenodo, January 19, 2019, pp.1-53, http://doi.org/10.5281/zenodo.2544527.
3. Inder J. Taneja, Palindromic-Type Pandigital Patterns in Pythagorean Triples, Zenodo, January 20, 2019, pp. 1-160, http://doi.org/10.5281/zenodo.2544551.
4. Inder J. Taneja, Generating Pythagorean Triples, Patterns, and Magic Squares, Zenodo, January 20, 2019, pp. 1-121, http://doi.org/10.5281/zenodo.2544555.
5. Inder J. Taneja, Patterns in Pythagorean Triples, Zenodo, March 13, 1-136, 2021, http://doi.org/10.5281/zenodo.4603197.
6. Inder J. Taneja, Pandigital-Type and Pythagorean Triples Patterns, Zenodo, March 17, 1-750, http://doi.org/10.5281/zenodo.4611511.

4. Semi-Selfie Representations

1. Inder J. Taneja, Patterns in Selfie and Semi-Selfie Numbers, Zenodo, February 6, 2019, pp. 1-51, http://doi.org/10.5281/zenodo.2563202.
2. Inder J. Taneja, Semi-Selfie Numbers, Zenodo, February 12, 2019, pp. 1-394, http://doi.org/10.5281/zenodo.2562390.
3. Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July 16, 2019, pp. 1-130, http://doi.org/10.5281/zenodo.3338366.

5. Selfie-Fractions and Patterns

1. Inder J. Taneja, Selfie Fractions: Addable, Subtractable, Dottable and Potentiable, Zenodo, March 24, 2019, pp. 1-260, http://doi.org/10.5281/zenodo.2604531.
2. Inder J. Taneja, Pandigital Equivalent Selfie Fractions, Zenodo, April 02, 2019, pp. 1-392, http://doi.org/10.5281/zenodo.2622028.
3. Inder J. Taneja, Repeated Digits Selfie Fractions: Two- and Three-Digits Numerators, Zenodo, September 12, 2019, pp. 1-1091, http://doi.org/10.5281/zenodo.3406655.
4. Inder J. Taneja, Different Digits Selfie Fractions: Two- and Three-Digits Numerators, Zenodo, September 12, 2019, pp. 1-337, http://doi.org/10.5281/zenodo.3474091
5. Inder J. Taneja, Different Digits Selfie Fractions: Four Digits Numerator, Zenodo, October 06, 2019, pp. 1-844, http://doi.org/10.5281/zenodo.3474267.
6. nder J. Taneja, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, http://doi.org/10.5281/zenodo.3520096.
7. Inder J. Taneja, Different Digits Selfie Fractions: Five Digits Numerator – Pandigital, Zenodo, October 06, 2019, pp. 1-362, http://doi.org/10.5281/zenodo.3474379.
8. Inder J. Taneja, Patterns in Splitted Selfie Fractions, Zenodo, July 30, 2023, pp. 1-122, http://doi.org/10.5281/zenodo.8197701

4. Narcissistic-Type Representations

1. Inder J. Taneja, Flexible Powers Narcissistic-Type Numbers, Zenodo, February 19, 2019, pp. 1-126, http://doi.org/10.5281/zenodo.2572770.
2. Inder J. Taneja, Fixed and Flexible Powers Narcissistic Numbers with Division, Zenodo, February 19, 2019, pp. 1-142, http://doi.org/10.5281/zenodo.2573047.
3. Inder J. Taneja, Fixed and Flexible Powers Narcissistic Numbers with Division (revised), Zenodo, May 11, 2020, pp. 1-201, http://doi.org/10.5281/zenodo.3820428.
4. Inder J. Taneja, Unified Study of Narcissistic Numbers without and with Division, Zenodo, Feb. 15, 2024, pp. 1-353, http://doi.org/10.5281/zenodo.10662872.