a(1) = 2, a(n+1) > a(n) is the smallest multiple of a(n) using only even digits.

Terms

a(0) =2a(1) =4a(2) =8a(3) =24a(4) =48a(5) =240a(6) =480a(7) =2400a(8) =4800a(9) =24000a(10) =48000a(11) =240000a(12) =480000a(13) =2400000a(14) =4800000a(15) =24000000a(16) =48000000a(17) =240000000a(18) =480000000a(19) =2400000000a(20) =4800000000a(21) =24000000000a(22) =48000000000a(23) =240000000000a(24) =480000000000