Jacobsthal numbers: Difference between revisions
Add C# implementation
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(Add C# implementation) |
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=={{header|C#}}==
{{trans|Java}}
<syntaxhighlight lang="C#">
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;
}
}
</syntaxhighlight>
{{out}}
<pre>
The first 30 Jacobsthal Numbers:
0 1 1 3 5
11 21 43 85 171
341 683 1365 2731 5461
10923 21845 43691 87381 174763
349525 699051 1398101 2796203 5592405
11184811 22369621 44739243 89478485 178956971
The first 30 Jacobsthal-Lucas Numbers:
2 1 5 7 17
31 65 127 257 511
1025 2047 4097 8191 16385
32767 65537 131071 262145 524287
1048577 2097151 4194305 8388607 16777217
33554431 67108865 134217727 268435457 536870911
The first 20 Jacobsthal oblong Numbers:
0 1 3 15 55
231 903 3655 14535 58311
232903 932295 3727815 14913991 59650503
238612935 954429895 3817763271 15270965703 61084037575
The first 10 Jacobsthal Primes:
3
5
11
43
683
2731
43691
174763
2796203
715827883
</pre>
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