Randp generates a random number between 1 and n, and will never generate that again; no loops or recursion! - http://paleyontology.com/AP_CS/randp.html

Randp.java

public class Randp {
  
  private int[] nums;
  private int numsLeft;
  
  public Randp(int n) {
    nums = new int[n];
    numsLeft = n;
  }
  
  public int nextInt() {
    if (numsLeft <= 0) return 0;
    
    int index = (int) (Math.random() * numsLeft);
    int num = nums[index];
    numsLeft--;
    if (nums[numsLeft] == 0) nums[index] = numsLeft + 1;
    else nums[index] = nums[numsLeft];
    
    if (num == 0) return index + 1;
    else return num;
  }
  
  public static void main(String[] args) {
    Randp r = new Randp(6);
    
    // 1-6
    System.out.println(r.nextInt());
    System.out.println(r.nextInt());
    System.out.println(r.nextInt());
    System.out.println(r.nextInt());
    System.out.println(r.nextInt());
    System.out.println(r.nextInt());
    
    // 0
    System.out.println(r.nextInt());
    System.out.println(r.nextInt());
  }
  
}

Randp.js

class Randp {

  constructor(n) {
    this.nums = [];
    this.numsLeft = n;
  }

  nextInt() {
    if (this.numsLeft <= 0) return 0;

    const index = Math.floor(Math.random() * this.numsLeft);
    const num = this.nums[index];
    this.numsLeft--;
    if (this.nums[this.numsLeft])
      this.nums[index] = this.nums[this.numsLeft];
    else
      this.nums[index] = this.numsLeft + 1;

    if (num) return num;
    else return index + 1;
  }

}

const r = new Randp(6);

// 1-6
console.log(r.nextInt());
console.log(r.nextInt());
console.log(r.nextInt());
console.log(r.nextInt());
console.log(r.nextInt());
console.log(r.nextInt());

// 0
console.log(r.nextInt());
console.log(r.nextInt());