Prolog - getting a list of friends of friends

I'm struggling to get a decent result,

I have some friends,

friend(a,b).
friend(a,b2).
friend(a,b3).
friend(b,c).
friend(c,d).
friend(d,e).  
friend(e,f).

Using findall(X,friend(a,X),List) I'm getting all direct friends of a

List=[b,b2,b3].

For example, I want to get a list of 3 level friends of a, for example, I want direct friends of a, the friends of friends of a (it means friends of b, b2, b3) and the friends of c. Getting the list:

List=[b,b2,b3,c,d].

I'm trying everything. I can only get direct friends or all friends of friends.

Help!!

Solution

The following stands for a 3-level friendship. As said in comments, if you want more, you might want to look for recursion.

% my friend is my friend
friend_of_friend(X,Y):-
    friend(X,Y).
% the friend of my friend is my friend
friend_of_friend(X,Y):-
    friend(X,Z),
    friend(Z,Y).
% the friend of the friend of my friend is my friend
friend_of_friend(X,Y):-
    friend(X,A),
    friend(A,B),
    friend(B,Y).

Then

findall(X, friend_of_friend(a,X), List).

Gives:

List = [b, b2, b3, c, d]

This would stand for infinite recursive friendship:

recursive_friend(X,Y):-
    friend(X,Y).
recursive_friend(X,Y):-
    friend(X,Z),
    recursive_friend(Z,Y).

And give:

List = [b, b2, b3, c, d, e, f]