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# Juggler Sequence

• Difficulty Level : Basic
• Last Updated : 29 May, 2021

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:
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

## C++

 // C++ implementation of Juggler Sequence#include using namespace std; // This function prints the juggler Sequencevoid 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 Codeint 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 Sequencevoid 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 functionint main(){    printJuggler(3);    printf("\n");    printJuggler(9);    return 0;}

## Java

 // Java implementation of Juggler Sequenceimport 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 functionpublic static void main (String[] args) {    printJuggler(3);    System.out.println();    printJuggler(9);    }}  //This code is contributed by Nikita Tiwari.

## Python

 import math #This function prints the juggler Sequencedef printJuggler(n) :    a = n         # print the first term    print a,         # 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,        a = b printJuggler(3)printprintJuggler(9) # This code is contributed by Nikita Tiwari.

## C#

 // C# implementation of Juggler Sequenceusing 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 Codepublic static void Main () {    printJuggler(3);    Console.WriteLine();    printJuggler(9);    }} // This code is contributed by Nitin Mittal

## PHP

 

## Javascript

 

Output:

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

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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