Given a number N. The task is to write a program to find the N-th term in the below series:
0, 2, 1, 3, 1, 5, 2, 7, 3, …
Examples:
Input: N = 5 Output: 1 Input: N = 10 Output: 11
When we look carefully at the series, we find that the series is a mixture of 2 series:
- Terms at odd positions in the given series forms fibonacci series.
- Terms at even positions in the given series forms a series of prime numbers.
Now, To solve the above-given problem, first check whether the input number N is even or odd.
- If it is odd, set N=(N/2) + 1(since there are Two series running parallelly) and find the Nth fibonacci number.
- If N is even, simply set N=N/2 and find Nth prime number.
Below is the implementation of above approach:
C++
// CPP program to find N-th term// in the series#include<bits/stdc++.h>#define MAX 1000using namespace std;// Function to find Nth Prime Numberint NthPrime(int n){ int count = 0; for (int i = 2; i <= MAX; i++) { int check = 0; for (int j = 2; j <= sqrt(i); j++) { if (i % j == 0) { check = 1; break; } } if (check == 0) count++; if (count == n) { return i; break; } }}// Function to find Nth Fibonacci Numberint NthFib(int n){ // Declare an array to store // Fibonacci numbers. int f[n + 2]; int i; // 0th and 1st number of the // series are 0 and 1 f[0] = 0; f[1] = 1; for (i = 2; i <= n; i++) { f[i] = f[i - 1] + f[i - 2]; } return f[n];}// Function to find N-th term// in the seriesvoid findNthTerm(int n){ // If n is even if (n % 2 == 0) { n = n / 2; n = NthPrime(n); cout << n << endl; } // If n is odd else { n = (n / 2) + 1; n = NthFib(n - 1); cout << n << endl; }}// Driver codeint main(){ int X = 5; findNthTerm(X); X = 10; findNthTerm(X); return 0;} |
Java
// Java program to find N-th // term in the seriesclass GFG {static int MAX = 1000;// Function to find Nth Prime Numberstatic int NthPrime(int n){int count = 0;int i;for (i = 2; i <= MAX; i++) { int check = 0; for (int j = 2; j <= Math.sqrt(i); j++) { if (i % j == 0) { check = 1; break; } } if (check == 0) count++; if (count == n) { return i; }} return 0;}// Function to find Nth Fibonacci Numberstatic int NthFib(int n){// Declare an array to store // Fibonacci numbers.int []f = new int[n + 2];int i;// 0th and 1st number of the// series are 0 and 1f[0] = 0;f[1] = 1;for (i = 2; i <= n; i++) { f[i] = f[i - 1] + f[i - 2];}return f[n];}// Function to find N-th term// in the seriesstatic void findNthTerm(int n){// If n is evenif (n % 2 == 0) { n = n / 2; n = NthPrime(n); System.out.println(n);}// If n is oddelse{ n = (n / 2) + 1; n = NthFib(n - 1); System.out.println(n);}}// Driver codepublic static void main(String[] args) { int X = 5; findNthTerm(X); X = 10; findNthTerm(X);}}// This code is contributed // by ChitraNayal |
Python 3
# Python 3 program to find N-th # term in the series # import sqrt method from math modulefrom math import sqrt# Globally declare constant valueMAX = 1000# Function to find Nth Prime Numberdef NthPrime(n) : count = 0 for i in range(2, MAX + 1) : check = 0 for j in range(2, int(sqrt(i)) + 1) : if i % j == 0 : check = 1 break if check == 0 : count += 1 if count == n : return i break# Function to find Nth Fibonacci Numberdef NthFib(n) : # Create a list of size n+2 # to store Fibonacci numbers. f = [0] * (n + 2) # 0th and 1st number of the # series are 0 and 1 f[0], f[1] = 0, 1 for i in range(2, n + 1) : f[i] = f[i - 1] + f[i - 2] return f[n]# Function to find N-th # term in the series def findNthTerm(n) : # If n is even if n % 2 == 0 : n //= 2 n = NthPrime(n) print(n) # If n is odd else : n = (n // 2) + 1 n = NthFib(n - 1) print(n)# Driver codeif __name__ == "__main__" : X = 5 # function calling findNthTerm(X) X = 10 findNthTerm(X) # This code is contributed by ANKITRAI1 |
C#
// C# program to find N-th term// in the seriesusing System;class GFG {static int MAX = 1000;// Function to find Nth Prime Numberstatic int NthPrime(int n){int count = 0;int i;for ( i = 2; i <= MAX; i++) { int check = 0; for (int j = 2; j <= Math.Sqrt(i); j++) { if (i % j == 0) { check = 1; break; } } if (check == 0) count++; if (count == n) { return i; }} return 0;}// Function to find Nth Fibonacci Numberstatic int NthFib(int n){ // Declare an array to store // Fibonacci numbers.int []f = new int[n + 2];int i;// 0th and 1st number of the// series are 0 and 1f[0] = 0;f[1] = 1;for (i = 2; i <= n; i++) { f[i] = f[i - 1] + f[i - 2];}return f[n];}// Function to find N-th term// in the seriesstatic void findNthTerm(int n){// If n is evenif (n % 2 == 0) { n = n / 2; n = NthPrime(n); Console.WriteLine(n);}// If n is oddelse{ n = (n / 2) + 1; n = NthFib(n - 1); Console.WriteLine(n);}}// Driver codepublic static void Main(){ int X = 5; findNthTerm(X); X = 10; findNthTerm(X);}}// This code is contributed // by ChitraNayal |
PHP
<?php// PHP program to find // N-th term in the series$MAX = 1000;// Function to find// Nth Prime Numberfunction NthPrime($n){ global $MAX; $count = 0; for ($i = 2; $i <= $MAX; $i++) { $check = 0; for ($j = 2; $j <= sqrt($i); $j++) { if ($i % $j == 0) { $check = 1; break; } } if ($check == 0) $count++; if ($count == $n) { return $i; break; } }}// Function to find// Nth Fibonacci Numberfunction NthFib($n){ // Declare an array to store // Fibonacci numbers. $f = array($n + 2); // 0th and 1st number of // the series are 0 and 1 $f[0] = 0; $f[1] = 1; for ($i = 2; $i <= $n; $i++) { $f[$i] = $f[$i - 1] + $f[$i - 2]; } return $f[$n];}// Function to find N-th // term in the seriesfunction findNthTerm($n){ // If n is even if ($n % 2 == 0) { $n = $n / 2; $n = NthPrime($n); echo $n . "\n"; } // If n is odd else { $n = ($n / 2) + 1; $n = NthFib($n - 1); echo $n . "\n"; }}// Driver code$X = 5;findNthTerm($X);$X = 10;findNthTerm($X);// This Code is contributed// by mits?> |
Javascript
<script>// JavaScript program to find N-th term// in the serieslet MAX =1000;// Function to find Nth Prime Numberfunction NthPrime( n){ let count = 0; for (let i = 2; i <= MAX; i++) { let check = 0; for (let j = 2; j <= Math.sqrt(i); j++) { if (i % j == 0) { check = 1; break; } } if (check == 0) count++; if (count == n) { return i; break; } }}// Function to find Nth Fibonacci Numberfunction NthFib( n){ // Declare an array to store // Fibonacci numbers. var f=new Int16Array(n+2).fill(0); let i; // 0th and 1st number of the // series are 0 and 1 f[0] = 0; f[1] = 1; for (i = 2; i <= n; i++) { f[i] = f[i - 1] + f[i - 2]; } return f[n];}// Function to find N-th term// in the seriesfunction findNthTerm( n){ // If n is even if (n % 2 == 0) { n = n / 2; n = NthPrime(n); document.write(n +"<br/>"); } // If n is odd else { n = parseInt(n / 2) + 1; n = NthFib(n - 1); document.write(n +"<br/>"); }}// Driver code let X = 5; findNthTerm(X); X = 10; findNthTerm(X);// This code contributed by aashish1995</script> |
Output:
1 11
Time Complexity: O(MAX*sqrt(MAX)), where MAX represents a defined constant.
Auxiliary Space: O(X), where X represents the given integer.
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!