Sylvester's sequence: Difference between revisions
Add C# implementation
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end
</syntaxhighlight>
=={{header|C#}}==
{{trans|Go}}
<syntaxhighlight lang="C#">
using System;
using System.Collections.Generic;
using System.Numerics;
public class SylvesterSequence
{
public static void Main(string[] args)
{
BigInteger one = BigInteger.One;
BigInteger two = new BigInteger(2);
List<BigInteger> sylvester = new List<BigInteger> { two };
BigInteger prod = two;
int count = 1;
while (count < 10)
{
BigInteger next = BigInteger.Add(prod, one);
sylvester.Add(next);
count++;
prod *= next;
}
Console.WriteLine("The first 10 terms in the Sylvester sequence are:");
foreach (var term in sylvester)
{
Console.WriteLine(term);
}
// Assuming a BigRational implementation or a workaround for the sum of reciprocals
BigInteger denominator = BigInteger.One;
foreach (var term in sylvester)
{
denominator = BigInteger.Multiply(denominator, term);
}
BigInteger numerator = BigInteger.Zero;
foreach (var term in sylvester)
{
numerator += denominator / term;
}
// Assuming you have a way to convert this to a decimal representation
Console.WriteLine("\nThe sum of their reciprocals as a rational number is:");
Console.WriteLine($"{numerator}/{denominator}");
// For the decimal representation, you might need to perform the division to a fixed number of decimal places
// This is a simplified approach and may not directly achieve 211 decimal places accurately
Console.WriteLine("\nThe sum of their reciprocals as a decimal number (to 211 places) is:");
Console.WriteLine(DecimalDivide(numerator, denominator, 210));
}
private static string DecimalDivide(BigInteger numerator, BigInteger denominator, int decimalPlaces)
{
// This is a basic implementation and might not be accurate for very large numbers or very high precision requirements
BigInteger quotient = BigInteger.Divide(numerator * BigInteger.Pow(10, decimalPlaces + 1), denominator);
string quotientStr = quotient.ToString();
string result = quotientStr.Substring(0, quotientStr.Length - decimalPlaces) + "." + quotientStr.Substring(quotientStr.Length - decimalPlaces);
return result;
}
}
</syntaxhighlight>
{{out}}
<pre>
The first 10 terms in the Sylvester sequence are:
2
3
7
43
1807
3263443
10650056950807
113423713055421844361000443
12864938683278671740537145998360961546653259485195807
165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
The sum of their reciprocals as a rational number is:
27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920805/27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920806
The sum of their reciprocals as a decimal number (to 211 places) is:
9.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999634
</pre>
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