令ap=bq,即3p+5=2q+4,得:q= 3p+1 2 = 2p+2+p?1 2 =p+1+ p?1 2 ,要使q为正整数,则只要p为正奇数,∵a1=3×1+5=8,a2n+1-a2n-1=3(2n+1)+5-3(2n-1)-5=6.∴数列{a2n-1}是以8为首项,6为公差的等差数列,取出数列{an}的奇数项,按原顺序排列,即构成数列{cn},∴cn=8+6(n-1)=6n+2.故答案为:cn=6n+2.