the badge similar to the square club badge on N1 is the super square club badge, where instead of members of the club being x^2, they are x^x, or x^^2, N1 has this badge because he is 2^N0, or 3^N0, or 4^N0, all the way up to N0^N0, or N0^^2, which fits the rule of being in super square club
me for making this project lol the creator of numberblock N0 for creating the design of numberblock N0