A066825 a(1) = 1; set of digits of a(n)^2 is a subset of the set of digits of a(n+1)^2.

1, 4, 13, 14, 31, 36, 54, 96, 113, 311, 487, 854, 1036, 1277, 1646, 3214, 3267, 3723, 4047, 4554, 4896, 5376, 10136, 13147, 13268, 16549, 20513, 21877, 25279, 26152, 27209, 28582, 31723, 32043, 32286, 33144, 35172, 35337, 35757, 35853