Data update

Task/Motzkin-numbers/JavaScript/motzkin-numbers.js

@@ -0,0 +1,88 @@
+// Motzkin Numbers Calculator
+
+class MotzkinNumbers {
+  static main() {
+    const count = 42;
+    const motzkins = this.motzkinNumbers(count);
+
+    console.log(" n        Motzkin[n]");
+    console.log("-----------------------------");
+
+    for (let n = 0; n < count; n++) {
+      const motzkin = motzkins[n];
+      const prime = this.isProbablePrime(motzkin);
+      const formatted = motzkin.toLocaleString('en-GB');
+      const line = `${n.toString().padStart(2)} ${formatted.padStart(23)}`;
+      console.log(line + (prime ? " prime" : ""));
+    }
+  }
+
+  static motzkinNumbers(size) {
+    const result = [];
+    result.push(1n);
+    result.push(1n);
+
+    for (let i = 2; i < size; i++) {
+      const nextMotzkin = result[i - 1] * BigInt(2 * i + 1)
+        + result[i - 2] * BigInt(3 * i - 3);
+      result.push(nextMotzkin / BigInt(i + 2));
+    }
+
+    return result;
+  }
+
+  static isProbablePrime(n) {
+    if (n < 2n) return false;
+    if (n === 2n || n === 3n) return true;
+    if (n % 2n === 0n) return false;
+
+    // Miller-Rabin primality test (simplified)
+    const witnesses = [2n, 3n, 5n, 7n, 11n, 13n, 17n, 19n, 23n, 29n];
+
+    for (const witness of witnesses) {
+      if (witness >= n) continue;
+      if (!this.millerRabinTest(n, witness)) return false;
+    }
+
+    return true;
+  }
+
+  static millerRabinTest(n, a) {
+    let d = n - 1n;
+    let r = 0;
+
+    while (d % 2n === 0n) {
+      d /= 2n;
+      r++;
+    }
+
+    let x = this.modPow(a, d, n);
+
+    if (x === 1n || x === n - 1n) return true;
+
+    for (let i = 0; i < r - 1; i++) {
+      x = (x * x) % n;
+      if (x === n - 1n) return true;
+    }
+
+    return false;
+  }
+
+  static modPow(base, exp, mod) {
+    let result = 1n;
+    base = base % mod;
+
+    while (exp > 0n) {
+      if (exp % 2n === 1n) {
+        result = (result * base) % mod;
+      }
+      exp = exp / 2n;
+      base = (base * base) % mod;
+    }
+
+    return result;
+  }
+}
+
+// Run the program
+MotzkinNumbers.main();