You don't need mod, loops or recursion to solve it. For instance:
local remove = table.remove
local insert = table.insert
local print = print
local sequence = {
false , false , 'Fizz' , false , 'Buzz',
'Fizz' , false , false , 'Fizz' , 'Buzz' ,
false , 'Fizz' , false , false , 'FizzBuzz'
}
local function o(v)
local name = remove(sequence,1)
insert(sequence,name)
print(name or v)
return v + 1
end
local function t(v)
return o(o(o(o(o(o(o(o(o(o(v))))))))))
end
local function h(v)
t(t(t(t(t(t(t(t(t(t(v))))))))))
end
h(1)
It does rely upon state (the sequence table) but even that could probably be worked around if Lua had a slice syntax.