So 11 is a Wieferich prime base 112 and [31] is a Wieferich prime base 374. I don't know whether to thank everybody for silently correcting it in stride, or grumble that no one is paying sufficient attention. Whichever the case, last week I put another one past you. At the very end of the long "inconvenient observation" message, (Apologies: In[378] is confusing because ConfinuedFractionK uses {{0,num},{1,den}} style matrices, but st uses {{den,num},{0,1}}.) should be {{den,num},{1,0}}. Neil has actually found an OEIS sequence corresponding to one of those fractalish output vs input patterns, but I now think these are the wrong place to focus. More important to the number theory is what gets produced vs exactly when, which varies with tweaking the conversion algorithm(s). --rwg