<!-- language-all: lang-java -->
# Java, <s>21</s> <s>57</s> 24 bytes

**[Try it online!][1]**

Golfed:

    n->(n-=n*2%3*20)>=0&n!=3

Ungolfed:

    import java.util.*;
    
    public class ChickenMcNuggetNumbers {
    
      private static final Set<Integer> FALSE_VALUES = new HashSet<>(Arrays.asList(
        new Integer[] { 0, 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23,
        25, 28, 31, 34, 37, 43 }));
    
      public static void main(String[] args) {
        for (int i = 0; i < 45; ++i) {
          System.out.println(i + " -> expected=" + !FALSE_VALUES.contains(i)
            + ", actual=" + f(n->(n-=n*2%3*20)>=0&n!=3, i));
        }
      }
    
      public static boolean f(java.util.function.Function<Integer, Boolean> f, int n) {
        return f.apply(n);
      }
    }


  [1]: https://tio.run/##ZZFfa9swFMXf/SlOCxtOopjETveH1IZstGyQ9cVsL2MMxZFdpc61ka7ThZLPnl1nCRvsQUic@9O590gbvdPjpjW0WT8d7bZtHGMjWtSxraPhPAiKWnuPj4@2eDL0pXjoqsrwQ7ddGefxEgRA6@xOs4FnzbZAaUnXyA3ffiY2lXEZ7hfL/O7nt8Xy612OFGSe8Un7x57JwoVzeu8j7ZfWcyh@OAHny99/4AUThalCrJAozBRuFN4qvBOxL0hlKvpUCtM3sqQ0fS@04LHosdCxsIlwiTCJ1GcJDoPB/DR8t6pl6PPsu8ausdWWwpydpUq6a1f5gQTt5yobh9ASw0qKyVy2W8xu5hiN7AUB8r1ns42ajiN5GeKaQosRrjHOYH61pmCzTq9Fufr3WaKiIZbGPhQroRV0wZ2uT2QZHmmchTROaRi/SobxZJClk9d0lSZHBdtH6Tsfgn79F2rVNLXRJC5/f7bsqGDbUHR/Plw@S@HDHzxDKdaSlS7RnOHOiU2k27beh3TqeggOx98