0
Julia, 51 bytes
n->diff(["_1238_4765"[digits(n)+1]...]).^2⊆[9,25]
Verification
julia> f=n->diff(["_1238_4765"[digits(n)+1]...]).^2⊆[9,25]
(anonymous function)
julia> map(f, (1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 18, 38, 61, 81, 294, 349, 381, 383, 729, 767, 38183, 38383, 18349276, 183492761, 618349...