- 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, Patterned Selfie Fractions, Zenodo, October 27, 2019, pp. 1-267, https://doi.org/10.5281/zenodo.3520096.
- Inder J. Taneja, Power-Type Semi-Selfie Numbers and Patterns, Zenodo, July 16, 2019, pp. 1-130, https://doi.org/10.5281/zenodo.3338366.
One thought on “103rd to 108th Days of Year: 13.04.23-18.04.23 – Crazy, Selfie-Fractions and Semi-Selfie Representations”
I’ve enjoyed your publications on 1 digit formulas since “Single Digit Representations of Natural Numbers” in 2015. If you’re interested in a similar project, or have tips on how to proceed, I’d love to hear from you, or see a paper.
The project I’ve been working on is the shortest *unique* representation. For example, in the previously mentioned work, we find 0= 1-1, 2-2, 3-3, etc; 5=(88-8)/(8+8),(99-9)/(9+9); and 10=(44-4)/4,(66-6)/6,(77-7)/7,etc. I believe, but have neither means nor skill to check, that the following are the shortest unique answers. 0=1^1-1 or 0=1*1-1, 0=2-2/2-2/2, 1=0^0,2-2/2. These were made and checked by pencil and paper. I also found numerous dead ends that were not unique. At this point, I pretty much abandoned the project. I suspect I need more math, an algorithm, and some serious computing power.