In previous works, authors wrote equality expressions in terms of 1 to 9 and 9 to 1 or 9 to 0 separated by single or double equality signs. These expressions are based on the idea of crazy representations of natural numbers. These equality expressions are based on basic operations along with factorial, square-root, Fibonacci sequence and triangular numbers values. These types of equalities, we called as crazy running equality expressions. This work is revised and enlarged version of author’s previous works, where the basic operations along with factorial, square-root are considered. It is not possible to write all the natural numbers in terms of crazy running equality expressions. Only the possible numbers are written. The work is up to 6 digits:
- 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
Link for download:
See few examples below:
Previous work for donwload:
- 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.
Recent work for download:
- 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
Results with Fibonacci Squence and Triangular numbers:
- 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, pp. 1-142, http://doi.org/10.5281/zenodo.2483327.