Patterns in Single-Letter and Single-Digit Representation of Natural Numbers

Patterns Single-Letter Representations

Below are few examples of patternized numbers written in terms of letter a

For more details of above examples, please refer author’s work:
Inder J. Taneja, Single Letter Patterned Representations and Fibonacci Sequence Values, Zenodo, Feb 06, 2019, 1-40, https://doi.org/10.5281/zenodo.2558522.

Below are few examples of patterns in single-letter representations of natural numbers

For more details of above examples, please refer author’s work:
Inder J. Taneja, Patterned Single Letter Representations of Natural Numbers, Zenodo, July 02, 2020, pp. 1-110, http://doi.org/10.5281/zenodo.3928507

Patterns Single-Digit Representations

Below are few examples of single-digit of some natural numbers.

More details of this kind of representations refer author’s work given in reference list.

Below are few examples of patterned single-digit representations:

For more details of above examples, please refer author’s work:
Inder J. Taneja, Patterns in Single-Digit Representations of Natural Numbers, Zenodo, January 19, 2026, pp. 1-284, https://doi.org/10.5281/zenodo.18296290

References

Single Digit

1. 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, Single Digits Representations of Numbers from 1 to 20000
2. Inder J. Taneja, Single Digit Representations of Natural Numbers From 1 to 5000, Zenodo, January 14, 2019, http://doi.org/10.5281/zenodo.2538893.
3. Inder J. Taneja, Single Digit Representations of Natural Numbers From 5001 to 10000, Zenodo, January 14, 2019, http://doi.org/10.5281/zenodo.2538897.
4. Inder J. Taneja, Single Digit Representations of Numbers From 10001 to 15000, Zenodo, January, 26, 2019, pp. 1-510, http://doi.org/10.5281/zenodo.2550414.
5. Inder J. Taneja, Single Digit Representations of Numbers From 15001 to 20000, Zenodo, January, 26, 2019, pp. 1-510, http://doi.org/10.5281/zenodo.2550440.
6. Inder J. Taneja, Patterned Single Digits Representations of Natural Numbers, Zenodo, July 04, 2020, pp. 1-590, http://doi.org/10.5281/zenodo.3930382.
7. Inder J. Taneja, Single Digit Representations of Natural Numbers From 20001 to 30000, Zenodo, March 21, 2022, pp. 1-1271, https://doi.org/10.5281/zenodo.6373774.
8. Inder J. Taneja, Single Digit Representations of Natural Numbers From 30001 to 40000, Zenodo, March 23, 2022, pp. 1-1269, https://doi.org/10.5281/zenodo.6379827.
9. Inder J. Taneja, Single Digit Representations of Natural Numbers From 40001 to 50000, Zenodo, March 23, 2022, pp. 1-1268, https://doi.org/10.5281/zenodo.6379875.
10. Inder J. Taneja, Patterns in Single-Digit Representations of Natural Numbers, Zenodo, January 19, 2026, pp. 1-284, https://doi.org/10.5281/zenodo.18296290

Single Letter

1. 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, Single Letter Representations Of Natural Numbers
2. 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.
3. 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.
4. Inder J. Taneja, Patterned Single Letter Representations of Natural Numbers, Zenodo, July 02, 2020, pp. 1-110, http://doi.org/10.5281/zenodo.3928507.