The sum of 1 + 7 + 13 + 19 +...+253 + 259 :

\(S=\left(259+1\right)\cdot\dfrac{\left(\dfrac{259-1}{6}+1\right)}{2}=5720\)

So the remainder is : \(\dfrac{5720}{6}=Q=953,R=2\)

Answer : 2.