Thue's Constant: In[186]:= 1/2 - Product[1 - 2^-2^k, {k, 0, ∞]}]/4 In[189]:= N[%186, 69] Out[189]= 0.412454033640107597783361368258455283089478374455769557573379415348794 Check: In[190]:= RealDigits[%, 16] Out[190]= {{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}, 0} Offer Dragon tasty dyadic rational: In[212]:= Round[%189, 2^-239] Out[212]= 364371599346514549123253464270244268067660704514265010052337909024213813/ 883423532389192164791648750371459257913741948437809479060803100646309888 In[213]:= $RecursionLimit = 9999; dragun@%212 Out[213]= {552141176700154938708639716987262633/ 1329227995784915872903807060280344576 + (449568033846806255846939851654337899 I)/ 1329227995784915872903807060280344576} D:=dragun[thue]. Then Re@D+Im@D == 7/15 + |D|² !! In[223]:= N[List @@ (Im[D] + Re[D] == 7/15 + Abs[D]^2) /. D -> %213[[1]], 33] Out[223]= {0.753602251625348009164368437081204, 0.753602251625348009164368437081204} —rwg