feat: add lucky numbers algorithm

Author: sarthakgupta1907-cell

Maths/LuckyNumbers.js

@@ -0,0 +1,29 @@
+/**
+ * @function getLuckyNumbers
+ * @description Lucky numbers are generated by a sieve similar to the
+ *   Sieve of Eratosthenes. Starting with natural numbers, every 2nd
+ *   number is removed, then every 3rd, then every 7th, etc.
+ *   Sequence: 1, 3, 7, 9, 13, 15, 21, 25, 31, 33...
+ * @param {number} limit - Upper limit to generate lucky numbers up to
+ * @returns {number[]} - Array of lucky numbers up to limit
+ * @see https://en.wikipedia.org/wiki/Lucky_number
+ * @example getLuckyNumbers(20) => [1, 3, 7, 9, 13, 15]
+ * @example getLuckyNumbers(50) => [1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49]
+ */
+const getLuckyNumbers = (limit) => {
+  if (!Number.isInteger(limit) || limit < 1) {
+    throw new TypeError('Input must be a positive integer')
+  }
+  let sieve = Array.from({ length: limit }, (_, i) => i + 1).filter(
+    (n) => n % 2 !== 0
+  )
+  let i = 1
+  while (i < sieve.length && sieve[i] <= sieve.length) {
+    const step = sieve[i]
+    sieve = sieve.filter((_, idx) => (idx + 1) % step !== 0)
+    i++
+  }
+  return sieve
+}
+
+export { getLuckyNumbers }

Maths/test/LuckyNumbers.test.js

@@ -0,0 +1,45 @@
+import { getLuckyNumbers } from '../LuckyNumbers.js'
+
+describe('getLuckyNumbers', () => {
+  test('getLuckyNumbers(1) returns [1]', () => {
+    expect(getLuckyNumbers(1)).toEqual([1])
+  })
+
+  test('getLuckyNumbers(10) returns [1, 3, 7, 9]', () => {
+    expect(getLuckyNumbers(10)).toEqual([1, 3, 7, 9])
+  })
+
+  test('getLuckyNumbers(20) returns correct list', () => {
+    expect(getLuckyNumbers(20)).toEqual([1, 3, 7, 9, 13, 15])
+  })
+
+  test('all results are within limit', () => {
+    const result = getLuckyNumbers(50)
+    expect(result.every((n) => n <= 50)).toBe(true)
+  })
+
+  test('result is sorted in ascending order', () => {
+    const result = getLuckyNumbers(50)
+    expect(result).toEqual([...result].sort((a, b) => a - b))
+  })
+
+  test('1 is always a lucky number', () => {
+    expect(getLuckyNumbers(10)[0]).toBe(1)
+  })
+
+  test('getLuckyNumbers(50) has correct count', () => {
+    expect(getLuckyNumbers(50)).toHaveLength(13)
+  })
+
+  test('throws TypeError for zero', () => {
+    expect(() => getLuckyNumbers(0)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => getLuckyNumbers(-10)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for float input', () => {
+    expect(() => getLuckyNumbers(10.5)).toThrow(TypeError)
+  })
+})