Find Array (Codeforces 1608A)
Tags: Math, constructive algorithms

Given $$$n$$$, find any array $$$a_1, a_2, \ldots, a_n$$$ of integers such that all of the following conditions hold: $$$1 \le a_i \le 10^9$$$ for every $$$i$$$ from $$$1$$$ to $$$n$$$.$$$a_1 < a_2 < \ldots <a_n$$$For every $$$i$$$ from $$$2$$$ to $$$n$$$, $$$a_i$$$ isn't divisible by $$$a_{i-1}$$$It can be shown that such an array always exists under the constraints of the problem.

Input: The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 100$$$). Description of the test cases follows.The only line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 1000$$$).It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^4$$$.

Output: For each test case print $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ — the array you found. If there are multiple arrays satisfying all the conditions, print any of them.

Note: In the first test case, array $$$[1]$$$ satisfies all the conditions.In the second test case, array $$$[2, 3]$$$ satisfies all the conditions, as $$$2<3$$$ and $$$3$$$ is not divisible by $$$2$$$.In the third test case, array $$$[111, 1111, 11111, 111111, 1111111, 11111111, 111111111]$$$ satisfies all the conditions, as it's increasing and $$$a_i$$$ isn't divisible by $$$a_{i-1}$$$ for any $$$i$$$ from $$$2$$$ to $$$7$$$.

Sample Inputs:
3
1
2
7

Sample Outputs:
1
2 3
111 1111 11111 111111 1111111 11111111 111111111

Solution (Python):
T = int(input())
for t in range(0, T):
    n = int(input())
    s = ''
    for i in range(2, n + 2):
        s += str(i)
        s += ' '
    print(s)

Solution (Python):
for _ in range(int(input())):
    a = int(input())
    for i in range(2, a + 2):
        print(i, end=' ')
    print()

Solution (Python):
t = int(input())
for i in range(t):
    x = int(input())
    lis = []
    j = 2
    while x > 0:
        lis.append(str(j))
        j = j + 1
        x = x - 1
    print(' '.join(lis))