257th Day of the Year: 13.09.24 – Crazy and Selfie-Fractions Representations, with Fixed Digits Repetitions Prime and Pythagorean Triples Patterns

References

1. Inder J. Taneja, Crazy Sequential Representation: Numbers from 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9, Jan. 2014, pp.1-161, http://arxiv.org/abs/1302.1479.
2. Site link: Crazy Representations of Natural Numbers – The 10958 Problem, https://inderjtaneja.com/2018/11/16/crazy-representations-of-natural-numbers-the-10958-problem.
3. Inder J. Taneja, Mathematical Representations for Days of the Year
4. Inder J. Taneja, Multiple Choices for Crazy Representations of Natural Numbers
5. Inder J. Taneja, Multiple Representations of Selfie Numbers – I (zenodo.org)
6. Inder J. Taneja, Permutable Powers Selfie Numbers, Zenodo, February 15, 2019, pp. 1-227,  http://doi.org/10.5281/zenodo.2566445.
7. Inder J. Taneja, Selfie Numbers: Basic Operations, Zenodo, March 26, 2019, pp. 1-134,  http://doi.org/10.5281/zenodo.2609143.
8. Inder J. Taneja, Factorial-Type Selfie Numbers in Digit’s Order, Zenodo, March 06, 2019, pp. 1-243,  http://doi.org/10.5281/zenodo.2585586.
9. Inder J. Taneja, Factorial-Type Selfie Numbers in Reverse Order of Digits, Zenodo, March 06, 2019, pp. 1-227, http://doi.org/10.5281/zenodo.2585599.
10. Inder J. Taneja, Square-Root Type Selfie Numbers, Zenodo, July 06, 2019, pp. 1-248,  http://doi.org/10.5281/zenodo.3352388
11. .Inder J. Taneja, Amicable Numbers With Patterns in Products and Powers (zenodo.org)
12. Inder J. Taneja, Patterns in Splitted Selfie Fractions (zenodo.org)
13. Inder J. Taneja, Unified Study of Narcissistic Numbers without and with Division (zenodo.org)Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns (zenodo.org)
14. Inder J. Taneja, Crazy Running Equality Expressions With Factorial and Square-Root (zenodo.org)
15. Inder J. Taneja, Pyramid-Type Representations of Natural Numbers (zenodo.org)
16. Inder J. Taneja, Pyramid-Type Representations of Natural Numbers from 1001 to 10000 (zenodo.org)
17. Inder J. Taneja,Factorial-Power Selfie Expressions (zenodo.org)
18. Inder J. Taneja, Selfie Expressions With Factorial, Fibonacci and Triangular Values (zenodo.org)
19. Inder J. Taneja, Fraction-Type Single Letter Representations of Natural Numbers From 1 to 11111, Zenodo, February 4, 2019, pp. 1-203, http://doi.org/10.5281/zenodo.2556902.
    • Site link: Single Letter Representations of Natural Numbers,  https://inderjtaneja.wordpress.com/2017/08/19/single-letter-representations-of-natural-numbers.
20. Inder J. Taneja, Single Letter Representations of Natural Numbers from 1 to 11111, Zenodo, February 5, 2019, pp. 1-133, http://doi.org/10.5281/zenodo.2557025.
21. Inder J. Taneja, Single Letter Patterned Representations and Fibonacci Sequence Values, Zenodo, February 6, 2019, pp. 1-40, http://doi.org/10.5281/zenodo.2558522.
22. Inder J. Taneja, Fixed Digits Repetitions Prime Patterns of Length 6 (zenodo.org)
23. 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.
24. Inder J. Taneja, Patterned Single Digits Representations of Natural Numbers, Zenodo, July 04, 2020, pp. 1-590, http://doi.org/10.5281/zenodo.3930382.