a(n) is the smallest divisor of the Motzkin number A001006(n) not already in the sequence.

Terms

a(0) =1a(1) =2a(2) =4a(3) =3a(4) =7a(5) =17a(6) =127a(7) =19a(8) =5a(9) =547a(10) =13a(11) =15511a(12) =15a(13) =6a(14) =9a(15) =284489a(16) =57a(17) =1089397a(18) =12a(19) =73a(20) =11a(21) =21a(22) =35a(23) =63a(24) =119a(25) =6417454619a(26) =38a(27) =107a(28) =31a(29) =1483