Recursion 3

Computer Science Level 2

Let $a_{0}=0$ , $a_{1}=1$ and $a_{n}= n^{a_{n-1}}$ where $n\ge2$ be a recursive function. Write a program that calculates the image value of any non-negative integer n.

Can you find $a_{4}$ mod $2015$ mod $20$ mod $15+2000$ ?

this problem is a part of the set Fundamental Programming

2013 2015 2016 2014

3 solutions

Arulx Z
Dec 24, 2015

I used a pretty straightforward algorithm (again) -

>>> def a(n):
        if n == 0:
            return 0
        if n == 1:
            return 1
        return n ** a(n - 1)
>>> a(4) % 2015 % 20 % 15 + 2000
2014

Zeeshan Ali
Dec 21, 2015

Here is an algorithm that may help you understand the recursive functions;

pow(n, p) starts
    if p is 1
        return n;
    else
        return n*pow(n, p-1);
pow(n, p) ends

func(n) starts
    if n is 0 or n is 1
        return n;
    else
        return pow(n, func(n-1));
func(n) ends

The first recursive function calculates the $p^{th}$ power a number n.
The second one is the actual required function that recursively determines the $n^{th}$ term of the sequence given.

Md Zuhair
Feb 22, 2019

#include<iostream>
#include<math.h>
using namespace std;
int recursion(int);
int recursion(int n)
{
    if(n==0)
    {
        return 0;
    }
    else if(n==1)
    {
        return 1;
    }
    else if(n>=2)
    {
        int z=pow(n,recursion(n-1));
        return z;
    }
}
int main()
{
    int n;
    cout<<"Enter n";
    cin>>n;
    cout<<"\n nth term"<<recursion(n);
    int k;
    k=((recursion(n)%2015)%20)%15+2000;
    cout<<endl<<k;
    return 0;
}

According to this code, k is the answer.

OUTPUT:-

Enter n4

nth term262144 2014

Process exited after 2.355 seconds with return value 0 Press any key to continue . . .

Recursion 3

this problem is a part of the set Fundamental Programming

3 solutions

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