EuclidMullin Sequence in JavaThe EuclidMullin Sequence is a mathematical sequence of prime numbers characterized by a recursive definition. In more technical terms, this sequence starts with the number 2 as its first term. Subsequent terms are generated by finding prime numbers that satisfy a specific condition. In this sequence, every new term is the smallest prime number. When you divide it by the previous term and add 1, the result is another prime number. Here's a more technical overview of the process:
Example 1: Input: N = 20 Output: 2 3 7 43 13 53 5 6221671 38709183810571 139 2801 11 17 5471 52662739 233 2207 1746860020068409 761 5403705334863907824909 Example 2: Input: N = 5 Output: 2 3 7 43 13 Example 3: Input: N = 8 Output: 2 3 7 43 13 53 5 6221671 Approach: Greedy AlgorithmIn the EuclidMullin sequence, the greedy algorithm works by repeatedly finding the smallest prime factor of (1 + product), where the product is the product of the previous terms in the sequence. It is the next term in the sequence. The algorithm then updates the product variable with the next term. The process is continued until the desired number of terms are created. Algorithm
ImplementationFilename: EuclidMullinSequence.java Output: EuclidMullin Sequence: 2 3 7 4313535 6221671 38709183810571 139 280111 17 5471 Time Complexity: The code has a time complexity of approximately O(N * sqrt(num)), where N is the number of terms to generate in the EuclidMullin Sequence. Auxiliary Space: The code has an auxiliary space complexity of O(1), meaning it uses a constant amount of memory that doesn't depend on the input size.
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