Question

In recreational mathematics, a Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. For example, in base 10, 18 is a Niven number since 18 is divisible by 1+8 = 9. Also, 12001 in base 3 is also a Niven number since the sum of the digits is 4 (which is 11 in base 3) divides 12001 (12001 = 1021 x 11).
Given a base b, any number n < b is trivially a Niven number. We will ignore this case.
Given a base b, and a positive integer T, find the lowest number L such that L, L+1, ..., L+T-1 are all Niven numbers but neither L-1 nor L+T are Niven numbers.
Input Format:
First line contains two integers, b and T
Output Format:
A single integer L such that L, L+1, ..., L+T-1 are all Niven numbers but neither L-1 nor L+T are Niven numbers.
Constraints:
2 ≤ b ≤ 10
1 < T < 7
Example 1
Input
10 4
Output
510
Explanation
510, 511, 512 and 513 are Niven numbers and 514 is not a Niven number. Also 509 is not a Niven number. It can be seen that for N < 510, no four consecutive numbers are Niven numbers.
Example 2
Input
5 5
Output
44
Explanation
44 in base 5 is equivalent to 24 in base 10. Clearly, sum of the digits is 8 = 13 in base 5 and 13 x 3 = 44 in base 5 and hence 44 is a Niven number. Similarly we can see 44+1 = 100, 101, 102 and 103 in base 5 are also Niven numbers. 104 is not a Niven number.

Answer 1

import java.util.*;
public class Niven {    int t;    public static void main(String args[]) {
        Niven obj = new Niven();        Scanner sc = new Scanner(System.in);        ArrayList<Integer> ls = new ArrayList<>();
        System.out.println("Enter integer t");        obj.t = sc.nextInt();
        System.out.println("Enter base b");        int base = sc.nextInt();        int x = 11;
        while (x < 10000) {            int cur = x;            for (int i = 0; i < obj.t; i++) {                ls.add(cur);                cur++;
            }
            boolean b = obj.check(ls, base);
            if (b == true) {                System.out.println(toBase(ls.get(0),base));                break;            }            ls.clear();            x++;        }    }
    public boolean check(ArrayList<Integer> ls, int base) {        int count = 0;        int sum;        int temp1 = 0;        for (int temp : ls) {            sum = 0;
            temp1 = temp;            String x = toBase(temp, base);            temp = Integer.parseInt(x);            
            while (temp > 0) {
                int var = temp % 10;                sum = sum + var;                temp = temp / 10;
            }                                    if (temp1 % sum == 0) {                count++;            }
        }
        if (count == t) {            sum = 0;            int first = ls.get(0) - 1;            int first1 = first;            String x2 = toBase(first, base);            first = Integer.parseInt(x2);            
            while (first > 0) {                int var1 = first % 10;                sum = sum + var1;                first = first / 10;            }            int sum1 = 0;            int last = ls.get(ls.size()-1) + 1;             int last1 = last;            String x3 = toBase(last, base);            last = Integer.parseInt(x3);                        while (last > 0) {                int var = last % 10;                sum1 = sum1 + var;                last = last / 10;            }                                                                       return !((first1 % sum == 0) && (last1 % sum1 == 0));        }
        return false;
    }
    public static String toBase(int n, int base) {        if (n == 0) {            return "0";        }        String binary = "";        while (n > 0) {            int rem = n % base;            binary = rem + binary;            n = n / base;        }
        return binary;    }}