Pears and Undiscovered Homophones!

Define Pearity as if a positive integer is $1 (mod 4)$ or $2 (mod 4)$ , or if it is $3 (mod 4)$ or $0 (mod 4)$ . If it is the former, define the integer to be ‎ Bosc , and if it is the latter, define the integer to be Bartlett . Take a Bosc . Divide it by $n$ , and get a Bartlett . Then divide it by $n+1$ and get another Bosc . Divide by $n+2$ and get $p$ (a Bartlett ). $p$ is a prime from $30$ to $40$ . Find if n is a Bartlett . DON'T GUESS!

Pearity is a Parody of Parity . Cool!