# Multiple Choices for Crazy Representations of Natural Numbers

#### ByInder J. Taneja

Mar 31, 2024

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:

The above work is up to natural numbers 300.000. More details are in the following two links

According to Link 1 we can write only with basic operations, the numbers up to 10957. The first number 10958 is not possible to write only with basic operations. Here we need some extra functions, such as factorial, square root etc.

The aim here is the write the numbers up to 10.000 with distinct functions, such as, square-root, factorial, quadratic (square), cubic, Triangular and Fibonacci, etc. See below two examples of numbers 100 and 218 written in six separate ways.

The above six numbers are from the following references:

1. Inder J. TanejaCrazy 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. Inder J. Taneja, Crazy Representations of Natural Numbers from 0 to 10000 Using Factorial and Square Root, Zenodo, April 07, 2024, pp. 1-260, http://doi.org/10.5281/zenodo.10938234.
3. Inder J. Taneja, Crazy Representations of Natural Numbers from 0 to 10000 Using Square Function, Zenodo, March 28, 2024, pp. 1-259, http://doi.org/10.5281/zenodo.10892480.
4. Inder J. Taneja, Crazy Representations of Natural Numbers from 0 to 10000 Using Cubic Function, Zenodo, March 30, 2024, pp. 1-259, https://doi.org/10.5281/zenodo.10899695.
5. Inder J. Taneja, Crazy Representations of Natural Numbers from 0 to 10000 Using Triangular Numbers, Zenodo, January, 16, 2024, pp. 1-259, https://doi.org/10.5281/zenodo.10516039.
6. Inder J. Taneja, Crazy Representations of Natural Numbers from 0 to 10000 Using Fibonacci Sequence Values, Zenodo, January, 14, 2024, pp. 1-261, https://doi.org/10.5281/zenodo.10501468.

### Days of the Year

Below are few examples of combination of all the six works representing as day of the year starting from day 100:

Let’s see below each case separately.

### Factorial and Square root

Below are few numbers written with factorial and square root. The total work is for natural numbers from 0 to 10000.

More details are in the following work:

• Inder J. Taneja, Crazy Representations of Natural Numbers from 0 to 10000 Using Factorial and Square Root, Zenodo, April 07, 2024, pp. 1-260, http://doi.org/10.5281/zenodo.10938234.

### Triangular Numbers

Below are few numbers written with triangular numbers. The total work is for natural numbers from 0 to 10000.

More details are in the following work:

### Fibonacci Sequence Values

Below are few numbers written with Fibonacci sequence values. The total work is for natural numbers from 0 to 10000.

More details are in the following work:

### Square Function

Below are few numbers written with square function. For knowledge, the square function is given by

Q(n)=n2, n is a natural number.

The total work is for natural numbers from 0 to 10000.

More details are in the following work:

### Cubic Function

Below are few numbers written with square function. For knowledge, the square function is given by

C(n)=n3, n is a natural number.

The total work is for natural numbers from 0 to 10000.

More details are in the following work: