Data update

Task/Jacobsthal-numbers/C-sharp/jacobsthal-numbers.cs

@@ -0,0 +1,155 @@
+using System;
+using System.Numerics;
+using System.Threading;
+
+public class JacobsthalNumbers
+{
+	private static BigInteger currentJacobsthal = 0;
+	private static int latestIndex = 0;
+	private static readonly BigInteger Three = new BigInteger(3);
+	private const int Certainty = 20;
+	public static void Main(string[] args)
+	{
+		Console.WriteLine("The first 30 Jacobsthal Numbers:");
+		for (int i = 0; i < 6; i++)
+		{
+			for (int k = 0; k < 5; k++)
+			{
+				Console.Write($"{JacobsthalNumber(i * 5 + k), 15}");
+			}
+
+			Console.WriteLine();
+		}
+
+		Console.WriteLine();
+		Console.WriteLine("The first 30 Jacobsthal-Lucas Numbers:");
+		for (int i = 0; i < 6; i++)
+		{
+			for (int k = 0; k < 5; k++)
+			{
+				Console.Write($"{JacobsthalLucasNumber(i * 5 + k), 15}");
+			}
+
+			Console.WriteLine();
+		}
+
+		Console.WriteLine();
+		Console.WriteLine("The first 20 Jacobsthal oblong Numbers:");
+		for (int i = 0; i < 4; i++)
+		{
+			for (int k = 0; k < 5; k++)
+			{
+				Console.Write($"{JacobsthalOblongNumber(i * 5 + k), 15}");
+			}
+
+			Console.WriteLine();
+		}
+
+		Console.WriteLine();
+		Console.WriteLine("The first 10 Jacobsthal Primes:");
+		for (int i = 0; i < 10; i++)
+		{
+			Console.WriteLine(JacobsthalPrimeNumber());
+		}
+	}
+
+	private static BigInteger JacobsthalNumber(int index)
+	{
+		BigInteger value = new BigInteger(ParityValue(index));
+		return ((BigInteger.Parse("1") << index) - value) / Three;
+	}
+
+	private static long JacobsthalLucasNumber(int index)
+	{
+		return (1L << index) + ParityValue(index);
+	}
+
+	private static long JacobsthalOblongNumber(int index)
+	{
+		BigInteger nextJacobsthal = JacobsthalNumber(index + 1);
+		long result = (long)(currentJacobsthal * nextJacobsthal);
+		currentJacobsthal = nextJacobsthal;
+		return result;
+	}
+
+	private static long JacobsthalPrimeNumber()
+	{
+		BigInteger candidate = JacobsthalNumber(latestIndex++);
+		while (!candidate.IsProbablyPrime(Certainty))
+		{
+			candidate = JacobsthalNumber(latestIndex++);
+		}
+
+		return (long)candidate;
+	}
+
+	private static int ParityValue(int index)
+	{
+		return (index & 1) == 0 ? +1 : -1;
+	}
+}
+
+
+public static class BigIntegerExtensions
+{
+    private static Random random = new Random();
+
+    public static bool IsProbablyPrime(this BigInteger source, int certainty)
+    {
+        if (source == 2 || source == 3)
+            return true;
+        if (source < 2 || source % 2 == 0)
+            return false;
+
+        BigInteger d = source - 1;
+        int s = 0;
+
+        while (d % 2 == 0)
+        {
+            d /= 2;
+            s += 1;
+        }
+
+        for (int i = 0; i < certainty; i++)
+        {
+            BigInteger a = RandomBigInteger(2, source - 2);
+            BigInteger x = BigInteger.ModPow(a, d, source);
+            if (x == 1 || x == source - 1)
+                continue;
+
+            for (int r = 1; r < s; r++)
+            {
+                x = BigInteger.ModPow(x, 2, source);
+                if (x == 1)
+                    return false;
+                if (x == source - 1)
+                    break;
+            }
+
+            if (x != source - 1)
+                return false;
+        }
+
+        return true;
+    }
+
+    private static BigInteger RandomBigInteger(BigInteger minValue, BigInteger maxValue)
+    {
+        if (minValue > maxValue)
+            throw new ArgumentException("minValue must be less than or equal to maxValue");
+
+        BigInteger range = maxValue - minValue + 1;
+        int length = range.ToByteArray().Length;
+        byte[] buffer = new byte[length];
+
+        BigInteger result;
+        do
+        {
+            random.NextBytes(buffer);
+            buffer[buffer.Length - 1] &= 0x7F; // Ensure non-negative
+            result = new BigInteger(buffer);
+        } while (result < minValue || result >= maxValue);
+
+        return result;
+    }
+}