Interestingly, there is a common pattern for fixed-points and cycles for different number lengths: numbers made of 4, 5 and 9. For example<p>length 3: fixed-point 495
length 5: 2-cycle containing 59994
length 6: fixed-point 59994<p>Similarly for digits 6, 1, 4, 7:<p>length 4: 6174
length 5: 4-cycle containing 61974
length 6: fixed-point 631764