Seems to me it would be cheaper to actually convert the number. 

sub test {
   my ($num, $base) = @_;
   while ($num > 0) {
      my $digit = $num % $base;
      return 0 if $digit > 1;
      $num = ($num - $digit)/$base;
   }

   return 1;
}

[download]

Takes at most floor(logb(n)) loop passes, just like what you were attempting.

In reply to Re: Can It Be Written In Base X With Only 1s And 0s by ikegami
in thread Can It Be Written In Base X With Only 1s And 0s by Limbic~Region

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