Given an integer N, the task is to print N integers ≤ 109 such that no two consecutive of these integers are co-prime and every 3 consecutive are co-prime.
Input: N = 3
Output: 6 15 10
Input: N = 4
Output: 6 15 35 14
- We can just multiply consecutive primes and for the last number just multiply the gcd(last, last-1) * 2. We do this so that the (n – 1)th number, nth and 1st number can also follow the property mentioned in the problem statement.
- Another important part of the problem is the fact that the numbers should be ≤ 109. If you just multiply consecutive prime numbers, after around 3700 numbers the value will cross 109. So we need to only use those prime numbers whose product wont cross 109.
- To do this in an efficient way, consider a small number of primes say the first 550 primes and select them in a way such that on making a product no number gets repeated. We first choose every prime consecutively and then choose the primes with an interval of 2 and then 3 and so on, doing that we already make sure that no number gets repeated.
So we will select
5, 11, 17, …
Next time, we can start with 7 and select,
7, 13, 19, …
Below is the implementation of the above approach:
6 15 35 14
- Expressing factorial n as sum of consecutive numbers
- Fibbinary Numbers (No consecutive 1s in binary)
- Express a number as sum of consecutive numbers
- 1 to n bit numbers with no consecutive 1s in binary representation.
- Check if a number can be expressed as a sum of consecutive numbers
- Find the number of consecutive zero at the end after multiplying n numbers
- Prove that atleast one of three consecutive even numbers is divisible by 6
- Count ways to express a number as sum of consecutive numbers
- Find the prime numbers which can written as sum of most consecutive primes
- Generate a list of n consecutive composite numbers (An interesting method)
- Print N lines of 4 numbers such that every pair among 4 numbers has a GCD K
- Composite XOR and Coprime AND
- Largest number less than or equal to N/2 which is coprime to N
- Finding a Non Transitive Coprime Triplet in a Range
- Partition first N natural number into two sets such that their sum is not coprime
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