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First Digit Four (Posted on 2009-08-08) Difficulty: 2 of 5
Determine the total number of base ten positive integers having the form 2N with the first digit (from the left) being 4, where N is a positive integer < 333.

See The Solution Submitted by K Sengupta    
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Solution statistics | Comment 2 of 3 |

UBASIC is much less expensive than Mathematica, and does the job.

The program tabulates, for the digits 1 through 9, their occurrence as the first digit of 2^N, for N=1 through 332. The statistics match pretty well those expected by Benford's Law.

list
    5   dim D(9)
   10   for N=1 to 332
   20     P=2^N
   30     Ps=cutspc(str(P))
   40     S=val(left(Ps,1))
   50     inc D(S)
   60   next
   70   for I=1 to 9:print I;D(I):next
OK
run
 1  99
 2  60
 3  40
 4  33
 5  27
 6  23
 7  17
 8  19
 9  14
OK


  Posted by Charlie on 2009-08-08 15:36:41
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