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Jacobsthal numbers (view source)

Revision as of 01:15, 4 February 2024

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Add C# implementation
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Line 1,102:
5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
</pre>
 
=={{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>
 
Line 2,361 ⟶ 2,558:
First 10 Jacobsthal prime numbers:
3 5 11 43 683 2731 43691 174763 2796203 715827883
</pre>
 
=={{header|PARI/GP}}==
<syntaxhighlight lang="PARI/GP">
\\ Define the Jacobsthal function
Jacobsthal(n) = (2^n - (-1)^n) / 3;
 
\\ Define the JacobsthalLucas function
JacobsthalLucas(n) = 2^n + (-1)^n;
 
\\ Define the JacobsthalOblong function
JacobsthalOblong(n) = Jacobsthal(n) * Jacobsthal(n + 1);
 
 
{
\\ Generate and print Jacobsthal numbers for 0 through 29
print(vector(30, n, Jacobsthal(n-1)));
 
\\ Generate and print JacobsthalLucas numbers for 0 through 29
print(vector(30, n, JacobsthalLucas(n-1)));
 
\\ Generate and print JacobsthalOblong numbers for 0 through 19
print(vector(20, n, JacobsthalOblong(n-1)));
 
\\ Find the first 20 prime numbers in the Jacobsthal sequence
myprimes = [];
i = 0;
while(#myprimes < 40,
if(isprime(Jacobsthal(i)), myprimes = concat(myprimes, [i, Jacobsthal(i)]));
i++;
);
 
for (i = 1, #myprimes\2, print(myprimes[2*i-1] " " myprimes[2*i]); );
}
</syntaxhighlight>
{{out}}
<pre>
[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]
[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]
[0, 1, 3, 15, 55, 231, 903, 3655, 14535, 58311, 232903, 932295, 3727815, 14913991, 59650503, 238612935, 954429895, 3817763271, 15270965703, 61084037575]
3 3
4 5
5 11
7 43
11 683
13 2731
17 43691
19 174763
23 2796203
31 715827883
43 2932031007403
61 768614336404564651
79 201487636602438195784363
101 845100400152152934331135470251
127 56713727820156410577229101238628035243
167 62357403192785191176690552862561408838653121833643
191 1046183622564446793972631570534611069350392574077339085483
199 267823007376498379256993682056860433753700498963798805883563
313 5562466239377370006237035693149875298444543026970449921737087520370363869220418099018130434731
347 95562442332919646317117537304253622533190207882011713489066201641121786503686867002917439712921903606443
 
</pre>
 
Line 3,016 ⟶ 3,274:
===Testing program===
≪ → func count
≪ { } 0 DO
'''DO''' DUP func IF EVAL THEN ROT SWAP + SWAP ELSE DROP END
'''IF''' EVAL '''THEN''' ROT SWAP + SWAP '''ELSE''' DROP '''END'''
1 +
UNTIL OVER SIZE count ≥1 END+
'''UNTIL''' OVER SIZE count ≥ '''END'''
DROP
DROP
≫ ≫
'<span style="color:blue">ASSRT</span>' STO
 
≪ <span style="color:blue">JCBN</span> 1 ≫ 30 <span style="color:blue">ASSRT</span>
≪ <span style="color:blue">JCBL</span> 1 ≫ 30 <span style="color:blue">ASSRT</span>
≪ <span style="color:blue">JCBO </span>1 ≫ 20 <span style="color:blue">ASSRT</span>
≪ DUP <span style="color:blue">JCBN PRIM?</span> ≫ 10 <span style="color:blue">ASSRT</span>
{{works with|Halcyon Calc|4.2.7}}
{{out}}
Aspen138
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