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# Juggler Sequence

• Difficulty Level : Basic
• Last Updated : 15 Mar, 2023

Juggler Sequence is a series of integer number in which the first term starts with a positive integer number a and the remaining terms are generated from the immediate previous term using the below recurrence relation : Juggler Sequence starting with number 3:
3, 5, 11, 36, 6, 2, 1
Juggler Sequence starting with number 9:
9, 27, 140, 11, 36, 6, 2, 1
Given a number n we have to print the Juggler Sequence for this number as the first term of the sequence.
Examples:

Input: 9
Output: 9, 27, 140, 11, 36, 6, 2, 1
next terms.

Input: 6
Output: 6, 2, 1
Recommended Practice

## C++

 // C++ implementation of Juggler Sequence #include  using namespace std;   // This function prints the juggler Sequence void printJuggler(long long n) {     long long a = n;       // print the first term     cout << a << " ";       // calculate terms until      // last term is not 1     while (a != 1)     {         long long b = 0;           // Check if previous term          // is even or odd         if (a % 2 == 0)               // calculate next term             b = floor(sqrt(a));           else               // for odd previous term              // calculate next term             b = floor(sqrt(a) *                        sqrt(a) * sqrt(a));           cout << b << " ";         a = b;     } }   // Driver Code int main() {     printJuggler(37);     cout <<"\n";     printJuggler(9);     return 0; }   // This code is contributed by shubhamsingh10

## C

 // C implementation of Juggler Sequence #include #include   // This function prints the juggler Sequence void printJuggler(int n) {     int a = n;       // print the first term     printf("%d ", a);       // calculate terms until last term is not 1     while (a != 1)     {         int b = 0;           // Check if previous term is even or odd         if (a%2 == 0)               // calculate next term             b  = floor(sqrt(a));           else               // for odd previous term calculate             // next term             b = floor(sqrt(a)*sqrt(a)*sqrt(a));           printf("%d ", b);         a = b;     } }   //driver program to test above function int main() {     printJuggler(3);     printf("\n");     printJuggler(9);     return 0; }

## Java

 // Java implementation of Juggler Sequence import java.io.*; import java.math.*;   class GFG {            // This function prints the juggler Sequence     static void printJuggler(int n)     {         int a = n;            // print the first term        System.out.print(a+" ");           // calculate terms until last term is not 1        while (a != 1)        {           int b = 0;                // Check if previous term is even or odd           if (a%2 == 0)                   // calculate next term                 b  = (int)Math.floor(Math.sqrt(a));               else                 // for odd previous term calculate             // next term                 b =(int) Math.floor(Math.sqrt(a) *                                Math.sqrt(a) * Math.sqrt(a));               System.out.print( b+" ");           a = b;         }     }   // Driver program to test above function public static void main (String[] args) {     printJuggler(3);     System.out.println();     printJuggler(9);     } }    //This code is contributed by Nikita Tiwari.

## Python3

 import math   #This function prints the juggler Sequence def printJuggler(n) :     a = n           # print the first term     print (a,end=" ")           # calculate terms until last term is not 1     while (a != 1) :         b = 0                   # Check if previous term is even or odd         if (a%2 == 0) :                           # calculate next term             b  = (int)(math.floor(math.sqrt(a)))            else :             # for odd previous term calculate             # next term             b = (int) (math.floor(math.sqrt(a)*math.sqrt(a)*                                          math.sqrt(a)))            print (b,end=" ")         a = b   printJuggler(3) print() printJuggler(9)   # This code is contributed by Nikita Tiwari.

## C#

 // C# implementation of Juggler Sequence using System;   class GFG {           // This function prints the juggler Sequence     static void printJuggler(int n)     {         int a = n;       // print the first term     Console.Write(a+" ");       // calculate terms until last term is not 1     while (a != 1)     {         int b = 0;               // Check if previous term is even or odd         if (a%2 == 0)                   // calculate next term                 b = (int)Math.Floor(Math.Sqrt(a));           else               // for odd previous term calculate             // next term                 b =(int) Math.Floor(Math.Sqrt(a) *                      Math.Sqrt(a) * Math.Sqrt(a));           Console.Write( b+" ");         a = b;         }     }   // Driver Code public static void Main () {     printJuggler(3);     Console.WriteLine();     printJuggler(9);     } }   // This code is contributed by Nitin Mittal

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Output:

3 5 11 36 6 2 1
9 27 140 11 36 6 2 1

Time complexity: O(nlogn) since using a single while loop and finding square root takes logarithmic time.

Space complexity: O(1) for constant variables

Important Points:

• The terms in Juggler Sequence first increase to a peak value and then start decreasing.
• The last term in Juggler Sequence is always 1.

Reference:
https://en.wikipedia.org/wiki/Juggler_sequence
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