this is logarithm problem ~!
I just multiply log10 to A= 2^n
double d = Math.log10(2);
int count =0;
for(int i=2; i<1000000000; i++){
double value = d* i;
double fp = value - (int) value;
double realValue = Math.pow(10, fp);
int result = (int)(realValue* 100d);
if(result== 123){
count++;
}
if(count == 678910){
System.out.println(i);
break; }
}