OMCPLP 2016 Problem 5

A numerical sequence is called lusophone if it satisfies the following three conditions: i) The first term of the sequence is number $1$ . ii) To obtain the next term of the sequence we can multiply the previous term by a positive prime number ( $2,3,5,7,11, ...$ ) or add $1$ . (iii) The last term of the sequence is the number $2016$ . For example: $1\overset{{\times 11}}{\to}11 \overset{{\times 61}}{\to} 671 \overset{{+1}}{\to}672 \overset{{\times 3}}{\to}2016$ How many Lusophone sequences exist in which (as in the example above) the add $1$ operation was used exactly once and not multiplied twice by the same prime number?