a(1) = 1; set of digits of a(n)^2 is a subset of the set of digits of a(n+1)^2.

Terms

a(0) =1a(1) =4a(2) =13a(3) =14a(4) =31a(5) =36a(6) =54a(7) =96a(8) =113a(9) =311a(10) =487a(11) =854a(12) =1036a(13) =1277a(14) =1646a(15) =3214a(16) =3267a(17) =3723a(18) =4047a(19) =4554a(20) =4896a(21) =5376a(22) =10136a(23) =13147a(24) =13268a(25) =16549a(26) =20513a(27) =21877a(28) =25279a(29) =26152