a(1) = 1, a(n) = smallest palindrome not included earlier such that a(1)+...+a(n) is a palindrome.

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =11a(5) =22a(6) =33a(7) =44a(8) =101a(9) =111a(10) =121a(11) =131a(12) =202a(13) =212a(14) =222a(15) =1001a(16) =1111a(17) =1221a(18) =1331a(19) =2002a(20) =2112a(21) =2222a(22) =10001a(23) =10101a(24) =10201a(25) =10301a(26) =11011a(27) =11111a(28) =12021a(29) =13031