Determine the respective last digit and the first digit (reading left to right) in the base ten expansion of


23²³²³²³

Remember that this is evaluated starting at the top-right and proceeding down and to the left.

The last few digits are:...6281606247 (WolframAlpha).

Computing the first digit directly exceeds free computing time.

However:

23^23   20880467999847912034355032910567     
(208)^23   206755325231194741614096313923167858253400517600346112   
(20880)^23  2258402623254084050800412717447474255438098159...    
(208804679)^23  2258402623254084050800412717447474255438098159...    
(22584)^23  137220784597010763616783092302409...  
(22584026)^23 13722441810163202418417765896222516547...
(225840262)^23  1372244460520242509008858232498435162473428... 

suggests that the first few digits are 1372244..., while computing no number longer than a mere 193 decimal digits.

Edited on November 16, 2013, 2:27 am

Posted by broll on 2013-11-16 01:38:05