Add Newman–Shanks–Williams prime (#2884) (#2955)

Co-authored-by: Andrii Siriak <siryaka@gmail.com>

src/main/java/com/thealgorithms/dynamicprogramming/NewManShanksPrime.java

@@ -0,0 +1,26 @@
+/** Author : Siddhant Swarup Mallick
+ * Github : https://github.com/siddhant2002
+ */
+
+
+/** Program description - To find the New Man Shanks Prime. */
+/** Wikipedia Link - https://en.wikipedia.org/wiki/Newman%E2%80%93Shanks%E2%80%93Williams_prime */
+
+package com.thealgorithms.dynamicprogramming;
+
+public class NewManShanksPrime {
+    public static boolean nthManShanksPrime(int n , int expected_answer)
+    {
+        int a[] = new int[n+1];
+        // array of n+1 size is initialized
+        a[0] = a[1] = 1;
+        // The 0th and 1st index position values are fixed. They are initialized as 1
+        for(int i=2;i<=n;i++)
+        {
+            a[i]=2*a[i-1]+a[i-2];
+        }
+        // The loop is continued till n
+        return a[n]==expected_answer;
+        // returns true if calculated answer matches with expected answer
+    }
+}