Find palindromic numbers in both binary and ternary bases

You are encouraged to solve this task according to the task description, using any language you may know.
Task

   Find and show (in decimal) the first six numbers (non-negative integers) that are   palindromes   in   both:
   base 2
   base 3
   Display   0   (zero) as the first number found, even though some other definitions ignore it.
   Optionally, show the decimal number found in its binary and ternary form.
   Show all output here.


It's permissible to assume the first two numbers and simply list them.



See also
   Sequence A60792,   numbers that are palindromic in bases 2 and 3 on The On-Line Encyclopedia of Integer Sequences.


using System;
using System.Collections.Generic;
using System.Linq;
 
public class FindPalindromicNumbers
{
    static void Main(string[] args)
    {
        var query =
            PalindromicTernaries()
            .Where(IsPalindromicBinary)
            .Take(6);
        foreach (var x in query) {
            Console.WriteLine("Decimal: " + x);
            Console.WriteLine("Ternary: " + ToTernary(x));
            Console.WriteLine("Binary: " + Convert.ToString(x, 2));
            Console.WriteLine();
        }
    }
 
    public static IEnumerable<long> PalindromicTernaries() {
        yield return 0;
        yield return 1;
        yield return 13;
        yield return 23;
 
        var f = new List<long> {0};
        long fMiddle = 9;
        while (true) {
            for (long edge = 1; edge < 3; edge++) {
                int i;
                do {
                    //construct the result
                    long result = fMiddle;
                    long fLeft = fMiddle * 3;
                    long fRight = fMiddle / 3;
                    for (int j = f.Count - 1; j >= 0; j--) {
                        result += (fLeft + fRight) * f[j];
                        fLeft *= 3;
                        fRight /= 3;
                    }
                    result += (fLeft + fRight) * edge;
                    yield return result;
 
                    //next permutation
                    for (i = f.Count - 1; i >= 0; i--) {
                        if (f[i] == 2) {
                            f[i] = 0;
                        } else {
                            f[i]++;
                            break;
                        }
                    }
                } while (i >= 0);
            }
            f.Add(0);
            fMiddle *= 3;
        }
    }
 
    public static bool IsPalindromicBinary(long number) {
        long n = number;
        long reverse = 0;
        while (n != 0) {
            reverse <<= 1;
            if ((n & 1) == 1) reverse++;
            n >>= 1;
        }
        return reverse == number;
    }
 
    public static string ToTernary(long n)
    {
        if (n == 0) return "0";
        string result = "";
        while (n > 0) {        {
            result = (n % 3) + result;
            n /= 3;
        }
        return result;
    }
 
}