public class Main
{
	public static void main(String[] args) {
    for (int i = 65535; i < 65545; i++) {
        System.out.println(
                i + ": " + getBinaryPalindrom(i) + " = " + Integer.toBinaryString(getBinaryPalindrom(i)));
    }
}
 
public static int getBinaryPalindrom(int N) {
    if (N < 4) {
        switch (N) {
            case 1:
                return 0;
            case 2:
                return 1;
            case 3:
                return 3;
        }
        throw new IndexOutOfBoundsException("You need to supply N >= 1");
    }
    // second highest to keep the right length (highest is always 1)
    final int bitAfterHighest = (N >>> (Integer.SIZE - Integer.numberOfLeadingZeros(N) - 2)) & 1;
    // now remove the second highest bit to get the left half of our palindrom
    final int leftHalf = (((N >>> (Integer.SIZE - Integer.numberOfLeadingZeros(N) - 1)) & 1) << (Integer.SIZE -
            Integer.numberOfLeadingZeros(N) - 2)) | ((N << (Integer.numberOfLeadingZeros(N) + 2)) >>> (Integer.numberOfLeadingZeros(N) + 2));
    // right half is just the left reversed
    final int rightHalf = Integer.reverse(leftHalf);
    if (Integer.numberOfLeadingZeros(leftHalf) < Integer.SIZE / 2) {
        throw new IndexOutOfBoundsException("To big to fit N=" + N + " into an int");
    }
    if (bitAfterHighest == 0) {
        // First uneven-length palindromes
        return (leftHalf << (Integer.SIZE - Integer.numberOfLeadingZeros(leftHalf)) - 1) | (rightHalf
                >>> Integer.numberOfTrailingZeros(rightHalf));
    } else {
        // Then even-length palindromes
        return (leftHalf << (Integer.SIZE - Integer.numberOfLeadingZeros(leftHalf))) | (rightHalf
                >>> Integer.numberOfTrailingZeros(rightHalf));
    }
}
}

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