feat: add Sylvester sequence algorithm

Maths/SylvesterSequence.js

@@ -0,0 +1,24 @@
+/**
+ * @function sylvesterSequence
+ * @description Sylvester's sequence is an integer sequence where each
+ *   term is the product of all previous terms plus one.
+ *   Sequence: 2, 3, 7, 43, 1807, 3263443...
+ * @param {number} n - Number of terms to generate (1-indexed count)
+ * @returns {number[]} - Array of first n terms of Sylvester's sequence
+ * @see https://en.wikipedia.org/wiki/Sylvester%27s_sequence
+ * @example sylvesterSequence(1) => [2]
+ * @example sylvesterSequence(4) => [2, 3, 7, 43]
+ */
+const sylvesterSequence = (n) => {
+  if (!Number.isInteger(n) || n < 1) {
+    throw new TypeError('Input must be a positive integer')
+  }
+  const sequence = [2]
+  for (let i = 1; i < n; i++) {
+    const prev = sequence[i - 1]
+    sequence.push(sequence.reduce((product, num) => product * num, 1) + 1)
+  }
+  return sequence
+}
+
+export { sylvesterSequence }

Maths/test/SylvesterSequence.test.js

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+import { sylvesterSequence } from '../SylvesterSequence.js'
+
+describe('sylvesterSequence', () => {
+  test('sylvesterSequence(1) returns [2]', () => {
+    expect(sylvesterSequence(1)).toEqual([2])
+  })
+
+  test('sylvesterSequence(2) returns [2, 3]', () => {
+    expect(sylvesterSequence(2)).toEqual([2, 3])
+  })
+
+  test('sylvesterSequence(3) returns [2, 3, 7]', () => {
+    expect(sylvesterSequence(3)).toEqual([2, 3, 7])
+  })
+
+  test('sylvesterSequence(4) returns [2, 3, 7, 43]', () => {
+    expect(sylvesterSequence(4)).toEqual([2, 3, 7, 43])
+  })
+
+  test('sylvesterSequence(5) returns [2, 3, 7, 43, 1807]', () => {
+    expect(sylvesterSequence(5)).toEqual([2, 3, 7, 43, 1807])
+  })
+
+  test('sylvesterSequence returns correct length', () => {
+    expect(sylvesterSequence(4)).toHaveLength(4)
+  })
+
+  test('sylvesterSequence starts with 2', () => {
+    expect(sylvesterSequence(3)[0]).toBe(2)
+  })
+
+  test('throws TypeError for zero', () => {
+    expect(() => sylvesterSequence(0)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => sylvesterSequence(-1)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for float input', () => {
+    expect(() => sylvesterSequence(1.5)).toThrow(TypeError)
+  })
+})