public List <string> Solve(List <Argument> input)
{
List <string> results = new List <string>();
int limit;
BigInteger result = 0;
Sequences sequences = new Sequences();
if (int.TryParse(input.First().Value.ToString(), out limit))
{
BigInteger fib = 1;
for (int i = 1; fib <= limit; i++)
{
if (fib % 2 == 0)
{
result += fib;
}
fib = sequences.GetFibonacciTerm(i);
}
}
results.Add(result.ToString());
return(results);
}
public void Problem41()
{
var primesUnder1B = new SortedSet <long>(
Sequences
.PrimesUnder(1_000_000)
.ToList()
);
var sum = new BigInteger(0);
for (int i = 1; i <= 9; i++)
{
sum += Functions.Permutations(i, i);
}
Console.WriteLine(sum);
for (int n = 9; n >= 4; n--)
{
// arithmetic series is going to be the sum of the series 1 to n.
// If the sum of the series 1 to n is divisible by 3, all
// permutations of 1 to n will be composites.
if (Series.Arithemtic(n) % 3 != 0)
{
var permutationsOf = Sequences.PermutationsOf(n, 0, 1);
foreach (var permutation in permutationsOf)
{
if (permutation % 2 != 0 && Functions.IsPrime(permutation))
{
Assert.That(permutation, Is.EqualTo(7_652_413));
return;
}
}
}
}
}
public void Problem7()
{
var answer
= Sequences.PrimeNumbers()
.Skip(10_000)
.First();
Assert.That(answer, Is.EqualTo(104743));
}
public void Problem21()
{
Func <int, dynamic> getDivisorsInfo = n =>
{
var uniqueDivisors = Sequences.UniqueDivisors(n).ToList();
return(new
{
Number = n,
AmicableSum = uniqueDivisors.Sum() - n
});
};
var divisors_cache = Enumerable.Range(1, 9_999)
.Select(getDivisorsInfo)
.ToList();
var d_cache = divisors_cache
.ToDictionary(x => x.Number, x => x.AmicableSum);
Func <int, int> d = (n) =>
{
if (d_cache.ContainsKey(n))
{
return(d_cache[n]);
}
else
{
var divisorsInfo = getDivisorsInfo(n);
divisors_cache.Add(divisorsInfo);
d_cache.Add(divisorsInfo.Number, divisorsInfo.AmicableSum);
return(divisorsInfo.AmicableSum);
}
};
var amicableNumbersUnder10000 = Enumerable.Range(1, 9_999)
.Where(a =>
{
var b = d(a);
return(a == d(b) && a != b);
})
.ToList();
var answer
= amicableNumbersUnder10000.Sum();
Assert.That(answer, Is.EqualTo(31_626));
}
public void Problem10()
{
long sum = 0;
foreach (var prime in Sequences.PrimeNumbers())
{
if (prime >= 2_000_000)
{
break;
}
sum += prime;
}
long answer = sum;
Assert.That(answer, Is.EqualTo(142_913_828_922));
}
public void Problem43()
{
// This is pretty slow.
Func <long, bool> meetsProperty = (permutation) =>
((permutation % 1_000_000_000) / 1_000_000) % 2 == 0 &&
((permutation % 100_000_000) / 100_000) % 3 == 0 &&
((permutation % 10_000_000) / 10_000) % 5 == 0 &&
((permutation % 1_000_000) / 1_000) % 7 == 0 &&
((permutation % 100_000) / 100) % 11 == 0 &&
((permutation % 10_000) / 10) % 13 == 0 &&
((permutation % 1_000)) % 17 == 0;
var sum = Sequences.PermutationsOf(10, 1, 1)
.Where(meetsProperty)
.Sum();
Console.WriteLine(sum);
}
public void Problem25()
{
var sequence = Sequences.Fibonacci(new BigInteger(1), new BigInteger(1));
var index = 0;
foreach (var number in sequence)
{
index++;
if (number.ToString().Length == 1000)
{
break;
}
}
Assert.That(index, Is.EqualTo(4_782));
}
public void Problem2()
{
long sum = 0;
foreach (long term in Sequences.Fibonacci(1, 2))
{
if (term >= 4_000_000)
{
break;
}
Console.WriteLine(term);
if (term % 2 == 0)
{
sum += term;
}
}
Console.WriteLine(sum);
}
public void Problem23()
{
var abundantNumbers = new SortedSet <int>();
for (int n = 12; n <= 28_123; n++)
{
var uniqueDivisors = Sequences.UniqueDivisors(n);
var sum = uniqueDivisors.Sum() - n;
if (sum > n)
{
abundantNumbers.Add(n);
}
}
var numbersThatAreNotSumOfTwoAbundantNumbers = new SortedSet <int>(
Enumerable.Range(1, 28_123)
.Select(x => x)
.ToList()
);
var abundantNumberList = abundantNumbers.ToList();
for (int i = 0; i < abundantNumberList.Count; i++)
{
var iNum = abundantNumberList[i];
for (int j = i; j < abundantNumberList.Count; j++)
{
var jNum = abundantNumberList[j];
var sum = iNum + jNum;
if (numbersThatAreNotSumOfTwoAbundantNumbers.Contains(sum))
{
numbersThatAreNotSumOfTwoAbundantNumbers.Remove(sum);
}
}
}
Assert.That(numbersThatAreNotSumOfTwoAbundantNumbers.Sum(), Is.EqualTo(4_179_871));
}
public void Problem32()
{
var permutations = Sequences.PermutationsOf(9, 0, 1)
.ToList();
SortedSet <long> products = new SortedSet <long>();
long sum = 0;
foreach (var permutation in permutations)
{
{
var left = permutation / 10_000_000;
var right = (permutation % 10_000_000) / 10_000;
var product = permutation % 10_000;
if (left * right == product)
{
if (!products.Contains(product))
{
products.Add(product);
}
}
}
{
var left = permutation / 100_000_000;
var right = (permutation % 100_000_000) / 10_000;
var product = permutation % 10_000;
if (left * right == product)
{
if (!products.Contains(product))
{
products.Add(product);
}
}
}
}
Assert.That(products.Sum(), Is.EqualTo(45_228));
}