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.
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