* Fred Lunnon <fred.lunnon@gmail.com> [Sep 06. 2014 15:22]: On 9/6/14, Bill Gosper <billgosper@gmail.com> wrote: [...] In[32]:= RealDigits[%, 16] Out[32]= {{6, 9, 9, 6, 9, 6, 6, 9, 9, 6, 6, 9, 6, 9, 9, 6, 9, 6, 6, 9, 6, 9, 9, 6, 6, 9, 9, 6, 9, 6, 6, 9, 8}, 0} ... >> That isn't the Thue-Morse sequence! Jörg>It is the TM seq. in hexadecimal. For a start, it contains both consecutive 0's and consecutive 1's ... ... as the TM seq. indeed does: https://oeis.org/A010060 WFL Thanks for speaking up, Jörg. I would have spent several days trying to get Fred's joke. Shifting the integer one bit and converting to base 4: In[46]:= IntegerDigits[ FromDigits[{6, 9, 9, 6, 9, 6, 6, 9, 9, 6, 6, 9, 6, 9, 9, 6, 9, 6, 6, 9, 6, 9, 9, 6, 6, 9, 9, 6, 9, 6, 6, 9, 9, 6, 6, 9, 6, 9, 9, 6, 6, 9, 9, 6, 9, 6, 6, 9, 6, 9, 9, 6, 9, 6, 6, 9, 9, 6, 6, 9, 6, 9, 9, 6}, 16]/2, 4] gives a "squarefree" (wasn't it once stutterfree?) sequence on four letters: Out[46]= {3, 1, 0, 3, 0, 2, 3, 1, 0, 2, 3, 0, 3, 1, 0, 3, 0, 2, 3, 0, 3, 1, 0, 2, 3, 1, 0, 3, 0, 2, 3, 1, 0, 2, 3, 0, 3, 1, 0, 2, 3, 1, 0, 3, 0, 2, 3, 0, 3, 1, 0, 3, 0, 2, 3, 1, 0, 2, 3, 0, 3, 1, 0, 3, 0, 2, 3, 0, 3, 1, 0, 2, 3, 1, 0, 3, 0, 2, 3, 0, 3, 1, 0, 3, 0, 2, 3, 1, 0, 2, 3, 0, 3, 1, 0, 2, 3, 1, 0, 3, 0, 2, 3, 1, 0, 2, 3, 0, 3, 1, 0, 3, 0, 2, 3, 0, 3, 1, 0, 2, 3, 1, 0, 3, 0, 2, 3} which retains its virtue after conflating 2&1: In[47]:= % /. {2 -> 1, 3 -> 2} Out[47]= {2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 0, 1, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 1, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 1, 2, 1, 0, 2, 0, 1, 2} Not obviously related to http://oeis.org/A086713 ? It might be nice to add this and a few variants to OEIS, but what is the likelihood of a match when a seeqr finds one independently? --rwg