Let's say $X = 6$ and $N = 100$ so the number$(P)$ from $1$ to $100$ when bitwise AND with $6$ gives same number$(P)$ are : $$0,2,4,6$$
for $X = 7$
$$0 1 2 3 4 5 6 7$$
I couldn't find better approach then brute forcing. I have also calculated all the number up to $17$ hoping to find some relation but don't seem to find one.
$$1: 0,1$$
$$2: 0,2$$
$$3: 0,1,2,3$$
$$4: 0,4$$
$$5: 0,1,4,5$$
$$6: 0,2,4,6$$
$$7: 0,1,2,3,4,5,6,7$$
$$8: 0,8$$
$$9: 0,1,8,9$$
$$10: 0,2,8,10$$
$$11: 0,1,2,3,8,9,10,11$$
$$12: 0,4,8,12$$
$$13: 0,1,4,5,6,8,10,12,14$$
$$14: 0,2,4,6,8,10,12,14$$
$$15: 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15$$
$$16: 0,16$$
$$17: 0,1,16,17$$
Also, $X$ can be greater then $N$.
How to approach this problem?