I understand that a continued fraction of the form: $g(n_1,n_2,n_3,n_4,n_5,\ldots)= n_1 + \cfrac{1}{n_2 + \cfrac{1}{n_3 + \cfrac{1}{n_4 + \cfrac{1}{n_5+\cdots} } } }$
gives a unique irrational number for every sequence of natural numbers $(n_1, n_2,n_3,n_4,n_5,...)$. I wish to however, restrict the output values of this continued fraction to say, an interval $(a,b) \in \mathbb R$. Is it possible to do so by somehow tweaking the fraction?