The Ramanujan's k(Ï„) function is defined as k(Ï„)=r(Ï„)r(2Ï„)2,
where r(Ï„) is the Rogers-Ramanujan continued fraction. Inspired by the
recent work of Park (2023) about the analogue of function k(Ï„) for the
Ramanujan cubic continued fraction, we study certain modular and arithmetic
properties of the function w(Ï„)=X(Ï„)X(3Ï„), where X(Ï„) is the
continued fraction of order six introduced by Vasuki, Bhaskar and Sharath
(2010). We consider w(Ï„) to be an analogue of k(Ï„) for the continued
fraction X(Ï„)