a(n) = smallest triangular number having no digit in common with the previous term, with a(1) = 1.

Terms

a(0) =1a(1) =3a(2) =6a(3) =10a(4) =28a(5) =36a(6) =45a(7) =66a(8) =78a(9) =91a(10) =253a(11) =406a(12) =528a(13) =630a(14) =741a(15) =820a(16) =946a(17) =1035a(18) =2278a(19) =3003a(20) =4186a(21) =5050a(22) =6216a(23) =7503a(24) =8128a(25) =9045a(26) =11628a(27) =33930a(28) =41616a(29) =52003