The newman-shanks-williams prime sequence is as follows1, 1, 3, 7, 17, 41...If we generalise the sequence items, we geta0=1 a1=1 an=2*a(n-1)+a(n-2)AlgorithmInitialise the number n.Initialise the first numbers of the sequence 1 and 1.Write a loop that iterates till n.Compute the next number using the previous numbers.Update the previous two numbers.Return ... Read More

The nesbitt's inequality is (a/(b + c)) + (b/(c + a)) + (c/(a + b))>= 1.5, a > 0, b > 0, c > 0Given three number, we need to check whether the three numbers satisfy Nesbitt's inequality or not.We can test whether three number are satisfied nesbitt's inequality or ... Read More

A neon number is a number where the sum of digits of the square of the number is equal to the number. Let's take an example.n = 9square = 81sum of digits of square = 8 + 1 = 9So, the number 9 is a neon number.We need to check ... Read More

We are given a number n, we need to find the nearest prime number that is less than n. We can find the number easily if we start checking from the n - 1. Let's see some examples.Input10Output7AlgorithmInitialise the number n.Write a loop that iterates from n - 1 to ... Read More

Numbers that are greater than 0 are called natural numbers. The natural number are1, 2, 3, 4, 5, 6, 7...AlgorithmInitialise the number n.Write a loop that iterates from 1 to n.Print the numbers.Increment the iterative variable.ImplementationFollowing is the implementation of the above algorithm in C++#include using namespace std; void ... Read More

The Narayana numbers can be expressed in terms of binomial expression $1/n\binom{n}{k} \binom{n}{k-1}$  Learn more about the Narayana number here.You are given the numbers n and k. Find the Narayana number. It's a straightforward problem having the combinations formula. Let's see the code.AlgorithmInitialise the numbers n and k.Find the Narayana ... Read More

A smart number is a number that contains at least three distinct prime factors. You are given a number N. Find the n-th smart number.The smart number series are30, 42, 60, 66, 70, 78...AlgorithmInitialise the number N.Initialise the count to 0.Write a function that checks whether the given number is ... Read More

In this tutorial, we are going to write a program that finds the n-th pentagonal number.A pentagonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. Refer to the wiki for better understanding.The n-th pentagonal number is (3 * n * n ... Read More

To find the n-th palindrome of k digits, we can iterate from the first k digits number till we find the n-th palindrome number. This approach is not efficient. You can try it yourself.Now, let's see the efficient approach to find the n-th palindrome of k digits.There are two halves ... Read More

The given series is 1, 17, 98, 354...If you clearly observe the series, you will find that the n-th number is equal to the 4 powers.Let's see the pattern. 1 = 1 ^ 4 17 = 1 ^ 4 + 2 ^ 4 98 = 1 ^ 4 + 2 ... Read More