# Juggler Sequence

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<stdio.h>
#include<math.h>

// 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.
```

## Python

```import math

#This function prints the juggler Sequence
def 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)
print
printJuggler(9)

# This code is contributed by Nikita Tiwari.
```

Output:

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

Important Points:

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

Reference:
https://en.wikipedia.org/wiki/Juggler_sequence
This article is contributed by Harsh Agarwal. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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