In 2013-2014, author (click here) wrote natural numbers in increasing and decreasing orders of 1 to 9 using only basic operations. See below some examples:
For more details and extension work by other see the following link:
- Inder J. Taneja, The Crazy Representations and 10958 Problem, https://inderjtaneja.com/2018/11/16/crazy-representations-of-natural-numbers-the-10958-problem/
The above study include the natural numbers till 30000. In some case factorials and or square-roots are used.
Recently, author wrote the above numbers till 100000 in increasing and decreasing orders of 1 to 9 and 9 to 1 using only the idea of factorials along with basic operations. Below are few examples:
These numbers are written in four parts. See the links below:
- Inder J. Taneja, Crazy Representations of Natural Numbers From 20001 to 40000, Zenodo, November 03, 2021, pp. 1-541, https://doi.org/10.5281/zenodo.5642776.
- Inder J. Taneja, Crazy Representations of Natural Numbers From 40001 to 60000, Zenodo, November 03, 2021, pp. 1-541, https://doi.org/10.5281/zenodo.5642826.
- Inder J. Taneja, Crazy Representations of Natural Numbers From 60001 to 80000, Zenodo, November 03, 2021, pp. 1-537, https://doi.org/10.5281/zenodo.5642896.
- Inder J. Taneja, Crazy Representations of Natural Numbers From 80001 to 100000, Zenodo, November 03, 2021, pp. 1-533, https://doi.org/10.5281/zenodo.5642929.
Recently, author wrote the above numbers from 100001 to 200000 in increasing and decreasing orders of 1 to 9 and 9 to 1 using only the idea of factorials along with basic operations. Below are few examples:
These numbers are written in five parts. See the links below:
- Inder J. Taneja, Crazy Representations of Natural Numbers From 100001 to 120000, Zenodo, November 03, 2021, pp. 1-541, https://doi.org/10.5281/zenodo.5773381.
- Inder J. Taneja, Crazy Representations of Natural Numbers From 120001 to 140000, Zenodo, November 03, 2021, pp. 1-541, https://doi.org/10.5281/zenodo.5773384.
- Inder J. Taneja, Crazy Representations of Natural Numbers From 140001 to 160000, Zenodo, November 03, 2021, pp. 1-537, https://doi.org/10.5281/zenodo.5773386.
- Inder J. Taneja, Crazy Representations of Natural Numbers From 160001 to 180000, Zenodo, November 03, 2021, pp. 1-533, https://doi.org/10.5281/zenodo.5773388.
- Inder J. Taneja, Crazy Representations of Natural Numbers From 180001 to 200000, Zenodo, November 03, 2021, pp. 1-533, https://doi.org/10.5281/zenodo.5773390.
The whole work is by use of basic operations along with factorials. There are few numbers not available by using factorials. In order to get the results we used an extra operation of square-root. These are following numbers:
These numbers are in increasing orders. Still there is one more numbers, i.e., 192398 not available even with factorial and square-root. We can get it alongwith other values by using Triangular number values and factorial. See below:
In case of decreasing orders we have all the numbers from 100001 to 200000.