feat: add Lucas number algorithm

Maths/LucasNumber.js

@@ -0,0 +1,26 @@
+/**
+ * @function lucasNumber
+ * @description Lucas numbers are an integer sequence similar to Fibonacci,
+ *   starting with 2 and 1. Each subsequent number is the sum of the two
+ *   preceding ones: 2, 1, 3, 4, 7, 11, 18, 29, ...
+ * @param {number} n - The position in the Lucas sequence (0-indexed)
+ * @returns {number} - The nth Lucas number
+ * @see https://en.wikipedia.org/wiki/Lucas_number
+ * @example lucasNumber(0) => 2
+ * @example lucasNumber(4) => 7
+ */
+const lucasNumber = (n) => {
+  if (!Number.isInteger(n) || n < 0) {
+    throw new TypeError('Input must be a non-negative integer')
+  }
+  if (n === 0) return 2
+  if (n === 1) return 1
+  let a = 2
+  let b = 1
+  for (let i = 2; i <= n; i++) {
+    ;[a, b] = [b, a + b]
+  }
+  return b
+}
+
+export { lucasNumber }

Maths/test/LucasNumber.test.js

@@ -0,0 +1,35 @@
+import { lucasNumber } from '../LucasNumber.js'
+
+describe('lucasNumber', () => {
+  test('lucasNumber(0) returns 2', () => {
+    expect(lucasNumber(0)).toBe(2)
+  })
+
+  test('lucasNumber(1) returns 1', () => {
+    expect(lucasNumber(1)).toBe(1)
+  })
+
+  test('lucasNumber(2) returns 3', () => {
+    expect(lucasNumber(2)).toBe(3)
+  })
+
+  test('lucasNumber(4) returns 7', () => {
+    expect(lucasNumber(4)).toBe(7)
+  })
+
+  test('lucasNumber(6) returns 18', () => {
+    expect(lucasNumber(6)).toBe(18)
+  })
+
+  test('lucasNumber(10) returns 123', () => {
+    expect(lucasNumber(10)).toBe(123)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => lucasNumber(-1)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for float input', () => {
+    expect(() => lucasNumber(1.5)).toThrow(TypeError)
+  })
+})