Exists.cs

using System;
using System.Linq;
					
public class Program
{
	public static bool Contains(int[] ints, int k)
    {
		if (ints.Length == 0)
            return false;
		
		if (ints.Length == 1)
			return k == ints[0];

        var position = ints.Length / 2;
        var middle = ints[position];
        if (k == middle)
			return true;

		// for perf we might want to use resize, copy or ArraySegment
        var scope = k > middle ? ints.Skip(position) : ints.Take(position);
        return Contains(scope.ToArray(), k);
    }
    
    public static bool Exists(int[] ints, int k)
    {
        return Contains(ints, k);
    }
	
	public static void Main()
	{
		Console.WriteLine(Exists(new int[]{},1) == false);
		Console.WriteLine(Exists(new int[]{0},1) == false);
		Console.WriteLine(Exists(new int[]{1},1) == true);
		Console.WriteLine(Exists(new int[]{0,1},1) == true);
		Console.WriteLine(Exists(new int[]{0,1},0) == true);
		Console.WriteLine(Exists(new int[]{0,2},1) == false);
		Console.WriteLine(Exists(new int[]{0,1,2},1) == true);
		Console.WriteLine(Exists(new int[]{0,1,2},2) == true);
		Console.WriteLine(Exists(new int[]{0,1,2,4},2) == true);
		Console.WriteLine(Exists(new int[]{0,1,2,3,4},4) == true);
		Console.WriteLine(Exists(new int[]{0,1,2,3,102},102) == true);
		Console.WriteLine(Exists(new int[]{0,1,2,3,102,102,102,102,102},102) == true);
	}
}

https://dotnetfiddle.net/N1nUCr