You can use a simple loop for example :

int n = 4;
String str = "";
for (int i = 1; i <= n; i++) {
    str+=i;
}

can we directly get int= 1234

In this case you can parse it like this :

int result = Integer.parseInt(str);

If you want to avoid this and get int from the begging you can use :

int n = 4;
int result = 0;
for (int i = 1; i <= n; i++) {
    result *= 10;
    result += i;
}

int n = 10;
StringBuffer s = new StringBuffer();
for(int i=1;i<=n;i++){
s = s.append(i); 
}
System.out.println(s.toString());

Note: Do not use String concatenation in for, instead it use StringBuilder.

Take a look at this question.

In your case n is a small value and because it is not so important. If n has a big value it will be a vast of memory.

Java 8 way

int n = 4;

StringBuilder sb = new StringBuilder();
IntStream.rangeClosed(1, n).forEach(sb::append);
String str = sb.toString();

Java 7 way

int n = 4;

StringBuilder sb = new StringBuilder();
for (int i = 1; i <= n; i++) {
    sb.append(i);
}
String str = sb.toString();