diff --git a/maths/collatz_sequence.ts b/maths/collatz_sequence.ts
new file mode 100644
index 00000000..fff660be
--- /dev/null
+++ b/maths/collatz_sequence.ts
@@ -0,0 +1,36 @@
+/**
+ * Generates the Collatz sequence for a given positive integer.
+ *
+ * The Collatz conjecture sequence is defined as follows:
+ * - Start with any positive integer `n`.
+ * - If `n` is even, divide it by 2.
+ * - If `n` is odd, multiply it by 3 and add 1.
+ * - Repeat the process with the new value of `n` until `n` equals 1.
+ *
+ * @param n - A positive integer to generate the Collatz sequence.
+ * @throws {Error} - Throws an error if `n` is not a positive integer.
+ * @returns {number[]} - The Collatz sequence starting from `n`.
+ *
+ * @example
+ * collatzSequence(5); // Returns: [5, 16, 8, 4, 2, 1]
+ * collatzSequence(10); // Returns: [10, 5, 16, 8, 4, 2, 1]
+ */
+export const collatzSequence = (n: number): number[] => {
+ if (n <= 0 || !Number.isInteger(n)) {
+ throw new Error('Sequence only defined for positive integers.')
+ }
+
+ const result: number[] = []
+
+ while (n !== 1) {
+ result.push(n)
+ if (n % 2 === 0) {
+ n /= 2
+ } else {
+ n = n * 3 + 1
+ }
+ }
+
+ result.push(1)
+ return result
+}
diff --git a/maths/test/collatz_sequence.test.ts b/maths/test/collatz_sequence.test.ts
new file mode 100644
index 00000000..2f65508e
--- /dev/null
+++ b/maths/test/collatz_sequence.test.ts
@@ -0,0 +1,39 @@
+import { collatzSequence } from '../collatz_sequence'
+
+describe('collatzSequence', () => {
+ test('should generate the correct Collatz sequence for n = 5', () => {
+ const result = collatzSequence(5)
+ expect(result).toEqual([5, 16, 8, 4, 2, 1])
+ })
+
+ test('should generate the correct Collatz sequence for n = 1', () => {
+ const result = collatzSequence(1)
+ expect(result).toEqual([1])
+ })
+
+ test('should handle large inputs correctly (n = 27)', () => {
+ const result = collatzSequence(27)
+ // The exact sequence for n = 27 is very long; check key parts
+ expect(result[0]).toBe(27)
+ expect(result[result.length - 1]).toBe(1)
+ expect(result.length).toBeGreaterThan(100)
+ })
+
+ test('should throw an error for n = 0', () => {
+ expect(() => collatzSequence(0)).toThrow(
+ 'Sequence only defined for positive integers.'
+ )
+ })
+
+ test('should throw an error for negative inputs (n = -5)', () => {
+ expect(() => collatzSequence(-5)).toThrow(
+ 'Sequence only defined for positive integers.'
+ )
+ })
+
+ test('should throw an error for non-integer inputs (n = 5.5)', () => {
+ expect(() => collatzSequence(5.5)).toThrow(
+ 'Sequence only defined for positive integers.'
+ )
+ })
+})
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