Given a number, find the numbers (smaller than or equal to n) which are both Fibonacci and prime.
Input : n = 40 Output: 2 3 5 13 Explanation : Here, range(upper limit) = 40 Fibonacci series upto n is, 1, 1, 2, 3, 5, 8, 13, 21, 34. Prime numbers in above series = 2, 3, 5, 13. Input : n = 100 Output: 2 3 5 13 89 Explanation : Here, range(upper limit) = 40 Fibonacci series upto n are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89. Prime numbers in Fibonacci upto n : 2, 3, 5, 13, 89.
An efficient solution is to use Sieve to generate all Prime numbers up to n. After we have generated prime numbers, we can quickly check if a prime is Fibonacci or not by using the property that a number is Fibonacci if it is of the form 5i2 + 4 or in the form 5i2 – 4. Refer this for details.
Below is the implementation of above steps
isSquare(5 * $i * $i – 4) > 0))
echo $i . ” “;
// Driver Code
$n = 30;
// This code is contributed by mits
2 3 5 13
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Improved By : Mithun Kumar