Find the cycle lengths of the permutation represented by the triangular numbers modulo powers of two; see https://math.stackexchange.com/questions/3491781.

Question3491781.java

package temp;

import java.util.ArrayList;
import java.util.BitSet;
import java.util.Collections;
import java.util.List;
import java.util.stream.Collectors;

public class Question3491781 {
    public static void main(String [] args) {
        for (int n = 4;;n <<= 1) {
            BitSet bitSet = new BitSet(n);
            List<Integer> cycleLengths = new ArrayList<Integer>();
            outer:
            for (;;) {
                int k = 0;
                while (bitSet.get(k))
                    if (++k == n)
                        break outer;
                int cycleLength = 0;
                int first = k;
                do {
                    bitSet.set(k);
                    k = ((k * (k + 1)) / 2) & (n - 1);
                    cycleLength++;
                } while (first != k);
                cycleLengths.add(cycleLength);
            }
            Collections.sort(cycleLengths);
            cycleLengths.remove(0);
            cycleLengths.remove(0);
            Collections.reverse(cycleLengths);
            System.out.println("    " + n + " : " + cycleLengths.stream().map(i -> i.toString()).collect(Collectors.joining(", ")));
        }
    }
}