feat(maths): juggler sequence

maths/juggler_sequence.ts

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+/**
+ * The juggler sequence is a integer sequence that starts with an positive integer a and the subsequent terms are
+ * described as following:
+ * if a_k is even:
+ *   a_k+1 = floor(sqrt(a_k))
+ * else:
+ *   a_k+1 = floor(sqrt(a_k^3))
+ *
+ * Time Complexity: linear (O(n))
+ *
+ * @param a The number to start with
+ * @param n The index of the searched number in the sequence.
+ * @returns The number at index n in the sequence.
+ * @see https://en.wikipedia.org/wiki/Juggler_sequence
+ */
+export const jugglerSequence = (a: number, n: number) => {
+  let k: number = a;
+  for (let i: number = 0; i < n; i++) {
+    k = Math.floor(Math.pow(k, (k % 2 === 0 ? 1 : 3) / 2));
+  }
+
+  return k;
+};

maths/test/juggler_sequence.test.ts

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+import { jugglerSequence } from '../juggler_sequence';
+
+describe('jugglerSequence', () => {
+  it.each([
+    [3, 3, 36],
+    [3, 5, 2],
+    [7, 3, 2],
+    [5, 1, 11],
+  ])('%i at index %i should equal %i', (a, n, k) => {
+    expect(jugglerSequence(a, n)).toBe(k);
+  });
+});