Odd Multiple Sequence Analyzer

This project implements a numerical search and filter algorithm in C. It generates a specific sequence of integers based on modular arithmetic constraints and employs a Reverse Output Strategy to present the data in descending order without the computational cost of a sorting algorithm.

🧮 Mathematical Constraints

The algorithm searches for a set of integers $S = {x_1, x_2, \dots, x_5}$ such that for every $x$:

1. Threshold: $x > 10$
2. Odd Parity: $x \equiv 1 \pmod 2$ (Odd Number)
3. Divisibility: $x \equiv 0 \pmod 3$ (Multiple of 3)

The resulting sequence (found in ascending order) is: $$S = {15, 21, 27, 33, 39}$$

⚙️ Algorithm Logic

1. Search Loop: Iterates starting from 11 ($x=11 \dots \infty$).
2. Filtering: Applies nested if conditions to validate constraints.
3. Storage: Valid numbers are stored in a fixed-size array (buffer[5]).
4. Reverse Rendering (Optimization):
   • Instead of running a sorting algorithm (like Bubble Sort) which costs $O(n^2)$, the program takes advantage of the fact that data is discovered in ascending order.
   • It iterates the array backwards (Index $4 \to 0$) to print the result "Largest to Smallest".
   • Time Complexity: $O(n)$ (Linear scan).

🚀 Usage

1. Compile the code:

   gcc main.c -o sequence_filter

2. Run the executable:

   ./sequence_filter

3. Output: 39 33 27 21 15

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This repository demonstrates conditional logic, array manipulation, and algorithmic efficiency in C.