$1,v_1=3$

$p_1=0$

$2$

$v_2=7$

$p_2=1$

$3$

$v_3=9$

$p_3=?$

$4$

$v_4=13$

$5$

$v_5=4$

$p_4=?$

$p_5=?$

$6p_6=$

$7p_7=$

$($a$)$ Recall that for any interval $i,p_i$ is the largest $ji{p}_{i}3i7j$ such that interval $jis$ compatible with $i.$ List the values for $p_i$ for $3i7.$