From http://www.math.grinnell.edu/~chamberl/courses/444/worksheets/high-precision... In[1]:= ContinuedFraction[Sum[Floor[E n]/2^n,{n,250000}],199]/.t_:>N@t /;t>9^99 Out[1]= {4,1,6,2,8,33818640,128,4294967296,4.034765434510795*10^118,2361183241434822606848,9.526820527087379*10^139,4.669359298953362*10^2270,2.143017214372535*10^301,1.000651735774753*10^2572,2.068391310070504*10^51881,2,1,12,1,6,3,2,5,7,1,230,3,2,1,1,1,3,1,1,9,4,2,4,2,15,1,66,1,3,2,5,1,124,2,1,5,1,1,1,6,14,9,5,5,19,2,6,1,2,2,3,1,6,4,2,1,15,8,1,5,1,2,1,18,1,3,1,2,1,2,2,1,8,1,3,5,6,2,1,3,1,2,1,3,1,3,1,1,2,6,5,2,1,1,10,6,5,1,1,22,1,7,4,5,1,2,1,3,6,1,1,14,1,1,4,1,10,1,10,5,8,7,1,2,3,1,1,7,1,1,18,1,1,21,1,5,8,3,6,21,3,4,1,58,2,2,1,2,47,235,1,1,1,1,1,3,66,6,2,8,1,2,1,2,2,3,2,1,1,34,7,8,1,10,5,2,1,3,2,1,2,3,1,1} In[476]:= ContinuedFraction[Sum[Floor[n π]/2^n,{n,500000}],199]/.n_:>N@n /;n>9^99//tim During evaluation of In[476]:= 37.877844,199 Out[476]= {6,127,638816050508714029100700827906,128,4.770094238300255*10^9930,10384593717069655257060992658440192,4.953549065688299*10^9964,5.144059450474297*10^9998,3.340033906683899*10^49925,1,126,638816050508714029100700827906,128,4.770094238300255*10^9930,10384593717069655257060992658440192,4.953549065688299*10^9964,1,6,33,1,7,4,1,1,950,3,1,1,1,5,1,1,36,7,1,4,4,1,4,1,1,2,2,1,6,8,2,1042,3,1,5,1,1,15,1,67,2,1,34,1,1,2,8,1,3,4,3,3,47,2,4,1,8,14,3,2,3,84,3,12,4,1,1,1,1,2,2,1,2,2,1,8,3,1,1,1,1,3,1,2,1,1,3,2,1,15,1,1,1,2,2,4,1,2,3,2,1,1,3,4,1,7,2,5,4,1,3,1,8,1,31,2,2,3,6,1,8,2,9,10,2,1,11,2,128,7,2,15,2,3,2,2,1,1,1,26,7,1,2,1,5,8,5,2,6,1,1,3,2,1,5,6,1,1,3,1,1,16,24,1,12,2,1,56,9,2,1,1,1,2,1,1,1,2,1,1,8,4,11} In[477]:= ContinuedFraction[Sum[Floor[n GoldenRatio]/2^n,{n,500000}],199]/.t_:>N@t/;t>9^99//tim During evaluation of In[477]:= 38.432713,199 Out[477]= {2,1,2,2,4,8,32,256,8192,2097152,17179869184,36028797018963968,618970019642690137449562112,22300745198530623141535718272648361505980416,13803492693581127574869511724554050904902217944340773110325048447598592,3.078281734093319*10^113,4.249103942534137*10^183,1.307993905256674*10^297,5.557802059636756*10^480,7.269571220627866*10^777,4.040283790268164*10^1258,2.937113076490272*10^2036,1.186677035312830*10^3295,3.485404637988021*10^5331,4.136049642673213*10^8626,1.441580660752191*10^13958,5.962449176788715*10^22584,1,4.682698892358224*10^32253,2,8,1,1,6,1,2,16,1,6,1,10,1,2,1,1,6,1,14,1,1,16,2,1,2,1,2,1,3,1,3,1,6,2,1,2,3,2,3,20,2,2,2,1,4,12,1,2,2,1,24,1,6,2,2,3,8,1,2,2,45,2,255,1,1,2,1,7,1,1,1,1,1,2,1,3,2,3,2,6,1,11,2,1,6,1,1,1,1,1,1,3,2,1,4,2,15,1,8,2,1,1,7,66,1,2,1,3,1,1,16,4,1,51,2,1,3,3,1,1,2,2,1,1,4,2,2,1,1,2,1,7,6,1,5,3,4,4,1,5,1,5,1,1,1,12,1,1,1,13,20,2,1,14,34,1,5,1,3,1,2,3,1,6,5,219,1,3,1,41} In[479]:= 2^Fibonacci@Range[-1,15] Out[479]= {2,1,2,2,4,8,32,256,8192,2097152,17179869184,36028797018963968,618970019642690137449562112,22300745198530623141535718272648361505980416,13803492693581127574869511724554050904902217944340773110325048447598592,307828173409331868845930000782371982852185463050511302093346042220669701339821957901673955116288403443801781174272,4249103942534136789516705652419749018636744941816255385595553105603228478886817941913300018121834285351114635889972008122772634701221657915276159830132698815550650166683145752253825024} (Shallit's?) --rwg