The rupee appreciated by 13 paise to 45 rupees 35 paise a dollar, continuing its rising streak for the sixth–straight session. The Indian currency was supported by higher opening on the stock market and dollar's weakness against other Asian units.Forex dealers said dollar's losses against other Asian currencies overseas and better opening at the stock markets kept the rupee's sentiment firm. The rupee had gained 11 paise to close at 45 rupees 49 paise a dollar in the previous session on persistent dollar sale by banks and corporates on the back of a weak greenback overseas.