If you use a prime near 62^n/2, udihash(range(1,10)) would still be unique but it would return a list that clearly has some linearity (V0001, 00002, V0003, 00004, V0005, 00006, V0007, 00008, V0009, 0000A, etc).

Using a prime near the golden ratio makes the list appear less linear (cJio3, EdRc6, qxAQ9, TGtEC, 5ac2F, huKqI, KE3eL, wXmSO, YrVGR, BBE4U).