a(n+1) is smallest square > a(n) having no digits in common with a(n), with a(0) = 0.

Terms

a(0) =0a(1) =1a(2) =4a(3) =9a(4) =16a(5) =25a(6) =36a(7) =49a(8) =81a(9) =225a(10) =361a(11) =400a(12) =529a(13) =676a(14) =841a(15) =900a(16) =1156a(17) =2209a(18) =3136a(19) =4225a(20) =6889a(21) =7225a(22) =8100a(23) =24336a(24) =58081a(25) =69696a(26) =70225a(27) =84681a(28) =90000a(29) =111556