public static long Solve()
{
long sum = 0;
List <string> pandigitals = EulerUtilities.Permute("0123456789");
int[] primes = new int[] { 1, 2, 3, 5, 7, 11, 13, 17 };
int subNumber;
bool success;
foreach (string pan in pandigitals)
{
if (pan[0].Equals("0"))
{
continue;
}
success = true;
for (int i = 0; i < pan.Length - 2; i++)
{
subNumber = int.Parse(pan.Substring(i, 3));
if ((subNumber % primes[i]) != 0)
{
success = false;
break;
}
}
if (success)
{
Console.WriteLine(pan);
sum += long.Parse(pan);
}
}
return(sum);
}
public static int Solve()
{
int min = 0, maxLength = 0;
HashSet <int> badNumbers = new HashSet <int>();
for (int start = 2; start <= 100000; start++)
{
List <int> chain = new List <int>();
List <int> factors = EulerUtilities.FindProperDivisors(start);
int current = factors.Sum();
while (current > 1 && current <= 1000000)
{
chain.Add(current);
factors = EulerUtilities.FindProperDivisors(current);
current = factors.Sum();
if (badNumbers.Contains(current))
{
break;
}
if (chain.Count > maxLength && chain.Contains(start))
{
maxLength = chain.Count;
min = chain.Min();
break;
}
if (chain.Contains(current))
{
badNumbers.Add(start);
break;
}
}
}
return(min);
}
//b has to be prime and positive for n^2 + a*n + b to give a positive prime for n=0
public static int Solve()
{
long[] bValues = EulerUtilities.GeneratePrimes(1000).ToArray();
int maxStreak = 0;
int aResult = 0, bResult = 0;
for (int a = -999; a < 0; a += 2)
{
for (int b = bValues.Length - 1; b >= 0; b--)
{
int n = 0, streak = 0, num;
num = Math.Abs(n * n + a * n + (int)bValues[b]);
while (EulerUtilities.IsPrime(num))
{
n++;
streak++;
num = Math.Abs(n * n + a * n + (int)bValues[b]);
}
if (streak > maxStreak)
{
aResult = a;
bResult = (int)bValues[b];
maxStreak = streak;
}
}
}
Console.WriteLine(aResult + ", " + bResult);
return(aResult * bResult);
}
public static string Solve()
{
List <long> primes = EulerUtilities.GeneratePrimes(10000);
primes.RemoveAll(x => x < 1000);
HashSet <string> permutationSet;
foreach (long prime in primes)
{
permutationSet = new HashSet <string>(EulerUtilities.Permute(prime.ToString()));
permutationSet.RemoveWhere(x => !primes.Contains(int.Parse(x)));
if (permutationSet.Count > 2 && !permutationSet.Contains("1487"))
{
for (int diff = 1; diff < 5000; diff++)
{
string one = (prime + diff).ToString();
string two = (prime + 2 * diff).ToString();
if (permutationSet.Contains(one) && permutationSet.Contains(two))
{
return(prime + one + two);
}
}
}
}
return("0");
}
public static int Solve()
{
List <int> primes = EulerUtilities.GeneratePrimes(1000000).ConvertAll(x => (int)x);
int[] ways;
int[] tempPrimes;
for (int i = 10; i < Int32.MaxValue; i++)
{
tempPrimes = primes.Where(x => x <= i).ToArray();
ways = new int[i + 1];
ways[0] = 1;
for (int prime = 0; prime < tempPrimes.Length; prime++)
{
for (int way = tempPrimes[prime]; way <= i; way++)
{
ways[way] += ways[way - tempPrimes[prime]];
}
}
if (ways[i] > 5000)
{
return(i);
}
}
return(0);
}
public static long Solve()
{
List <long> pentas = new List <long>();
pentas.Add(1);
for (long i = 2; i < 10000; i++)
{
pentas.Add(i * (3 * i - 1) / 2);
}
long difference = 0;
long minDifference = long.MaxValue;
for (int low = 0; low < pentas.Count; low++)
{
for (int high = low; high < pentas.Count; high++)
{
difference = pentas[high] - pentas[low];
if (EulerUtilities.IsPentagonalNumber(pentas[low] + pentas[high]) && EulerUtilities.IsPentagonalNumber(pentas[high] - pentas[low]) && difference < minDifference)
{
minDifference = difference;
}
}
}
return(minDifference);
}
public static int Solve()
{
int count = 0;
string text = File.ReadAllText(@"..\..\txt\Problem042Text.txt");
string[] words = text.Split(',');
for (int i = 0; i < words.Length; i++)
{
words[i] = words[i].Replace("\"", "");
}
int wordSum;
foreach (string word in words)
{
wordSum = 0;
foreach (char c in word)
{
wordSum += ((int)c) - 64;
}
if (EulerUtilities.IsTriangleNumber(wordSum))
{
count++;
}
}
return(count);
}
public static int Solve()
{
int finalSum = 0;
List <int> positiveIntegers = new List <int>(Enumerable.Range(1, 28123));
List <int> abundantIntegers = new List <int>();
for (int i = 2; i < 28123; i++)
{
if (EulerUtilities.FindProperDivisors(i).Sum() > i)
{
abundantIntegers.Add(i);
}
}
int sum;
for (int outer = 0; outer < abundantIntegers.Count; outer++)
{
for (int inner = outer; inner < abundantIntegers.Count; inner++)
{
sum = abundantIntegers[outer] + abundantIntegers[inner];
if (sum > 28123)
{
break;
}
else
{
positiveIntegers.Remove(sum);
}
}
}
finalSum = positiveIntegers.Sum();
return(finalSum);
}
public static int Solve()
{
int limit = 100000000;
int count = 0;
bool mEven = true;
for (int m = 2; m <= (int)((Math.Sqrt(1 + 2 * limit) - 1) / 2); m++)
{
int n = mEven ? 1 : 2;
mEven = !mEven;
int m2 = m * m;
int mn = 2 * m * n;
while (n < m && (2 * m2 + mn) <= limit)
{
if (EulerUtilities.GreatestCommonDivisor(n, m) == 1)
{
int a = mn;
int b = m2 - n * n;
int c = m2 + n * n;
if (c % (b - a) == 0)
{
count += (limit / (a + b + c));
}
}
n += 2;
mn = 2 * m * n;
}
}
return(count);
}
public static int Solve()
{
int limit = 1000000000;
primes = EulerUtilities.GeneratePrimes(100).ConvertAll(x => (int)x);
return(HammingCount(1, 0, limit));
}
public static int Solve()
{
int count = 0;
for (int d = 2; d <= 12000; d++)
{
for (int n = 1; n < d; n++)
{
if (n * 2 >= d)
{
break;
}
if (n * 3 <= d)
{
continue;
}
if (n % 2 == 0 && d % 2 == 0)
{
continue;
}
if (EulerUtilities.GreatestCommonDivisor(n, d) == 1)
{
count++;
}
}
}
return(count);
}
public static int Solve()
{
List <long> primesLong = EulerUtilities.GeneratePrimes(1000000);
List <int> primes = primesLong.ConvertAll(x => (int)x);
int maxStreak = 1, maxPrime = 0;
int currentStreak, current;
for (int start = 0; start < primes.Count; start++)
{
currentStreak = 1;
current = 0;
for (int consec = start; consec < primes.Count; consec++)
{
current += primes[consec];
if (current > 1000000)
{
break;
}
if (currentStreak > maxStreak && primes.Contains(current))
{
maxStreak = currentStreak;
maxPrime = current;
}
currentStreak++;
}
}
return(maxPrime);
}
public static int Solve()
{
int Lmax = 1500000;
int[] counts = new int[Lmax + 1];
for (int i = 2; i < Math.Sqrt(Lmax / 2); i++)
{
for (int j = 1; j < i; j++)
{
if ((i + j) % 2 == 1 && EulerUtilities.GreatestCommonDivisor(i, j) == 1)
{
int a = (int)(Math.Pow(i, 2) - Math.Pow(j, 2));
int b = 2 * i * j;
int c = (int)(Math.Pow(i, 2) + Math.Pow(j, 2));
int L = a + b + c;
for (int k = 1; k *L < Lmax; k++)
{
counts[k * L] += 1;
}
}
}
}
return(counts.Where(x => x == 1).Count());
}
public static int Solve()
{
EulerUtilities.LoadPrimes(int.MaxValue / 10);
HashSet <long> uniques;
int streak = 0, answer = 0;
for (int i = 646; i < int.MaxValue; i++)
{
uniques = EulerUtilities.UniquePrimeFactors((long)i);
if (uniques.Count == 4)
{
streak++;
if (streak == 4)
{
answer = i - 3;
break;
}
}
else
{
streak = 0;
}
}
return(answer);
}
public static int Solve()
{
int limit = 5000000;
List <int> primes = EulerUtilities.GeneratePrimesSmall(2 * limit);
int count = 0;
for (long n = 2; n <= limit; n++)
{
long val = 2 * n * n - 1;
int bound = (int)Math.Sqrt(val);
int i = 1;
int prime = primes[i];
bool isPrime = true;
while (prime <= bound)
{
if (val % prime == 0)
{
isPrime = false;
break;
}
i++;
prime = primes[i];
}
if (isPrime)
{
count++;
}
}
return(count);
}
public static int Solve()
{
int max = 0, count, maxPerim = 0;
double c, perimeter;
for (int perim = 120; perim <= 1000; perim++)
{
count = 0;
for (int a = 1; a <= perim / 2; a++)
{
for (int b = 1; b <= perim / 2; b++)
{
c = Math.Sqrt(Math.Pow(a, 2) + Math.Pow(b, 2));
perimeter = a + b + c;
if (perimeter == perim && EulerUtilities.IsWholeNumber(perimeter))
{
count++;
}
}
}
if (count > max)
{
max = count;
maxPerim = perim;
}
}
return(maxPerim);
}
public static long Solve()
{
double goal = 15499.0 / 94744.0;
List <int> primes = EulerUtilities.GeneratePrimes(100).ConvertAll(x => (int)x);
EulerUtilities.LoadPrimes(100000000);
long res = 1;
for (int i = 0; i < primes.Count; i++)
{
res *= primes[i];
if ((double)EulerUtilities.TotientCount(res) / (res - 1) < goal)
{
res /= primes[i];
break;
}
}
for (int i = 1; ; i++)
{
long r = res * i;
if ((double)EulerUtilities.TotientCount(r) / (r - 1) < goal)
{
return(r);
}
}
return(0);
}
public static int Solve()
{
int limit = (int)Math.Pow(10, 4);
int sum = 0;
bool mEven = true;
for (int m = 2; m <= limit; m++)
{
int n = mEven ? 1 : 2;
mEven = !mEven;
int m2 = m * m;
int mn = 2 * m * n;
while (n < m && (2 * m2 + mn) <= limit)
{
if (EulerUtilities.GreatestCommonDivisor(n, m) == 1)
{
int a = mn;
int b = m2 - n * n;
int c = m2 + n * n;
if (c % (b - a) == 0)
{
sum += (limit / (a + b + c));
}
}
n += 2;
mn = 2 * m * n;
}
}
return(sum);
}
public static long Solve()
{
List <long> primes = EulerUtilities.GeneratePrimes(100000);
primes.RemoveAll(x => (x < 1000 && x > 10000));
double minRatio = double.MaxValue;
long minNumber = 0;
for (int i = 0; i < primes.Count; i++)
{
for (int j = i + 1; j < primes.Count; j++)
{
long num = (primes[i] * primes[j]);
long totient = (primes[i] - 1) * (primes[j] - 1);
double ratio = ((double)num) / totient;
if (num > 10000000)
{
break;
}
if (ratio < minRatio && EulerUtilities.IsPermutation(num.ToString(), totient.ToString()))
{
minRatio = ratio;
minNumber = num;
}
}
}
return(minNumber);
}
public static long Solve()
{
int limit = 1000000000;
primes = EulerUtilities.GeneratePrimesSmall(limit);
HashSet <long> admissibles = GenerateAdmissible(limit);
BitArray primeBits = new BitArray(limit, false);
foreach (int p in primes)
{
primeBits[p] = true;
}
HashSet <int> uniques = new HashSet <int>();
foreach (long admiss in admissibles)
{
for (int i = 2; i < int.MaxValue; i++)
{
if (primeBits[(int)admiss + i])
{
uniques.Add(i);
break;
}
}
}
return(uniques.Sum());
}
public static int Solve()
{
List <int> successfulStarts = new List <int>();
List <int> chain = new List <int>();
for (int i = 3; i < 1000000; i++)
{
chain.Add(i);
int current = (int)i.ToString().Sum(x => EulerUtilities.Factorial(x - 48));
while (!chain.Contains(current))
{
chain.Add(current);
current = (int)current.ToString().Sum(x => EulerUtilities.Factorial(x - 48));
if (chain.Count == 60 && chain.Contains(current))
{
successfulStarts.Add(i);
}
if (chain.Count > 60)
{
break;
}
}
chain.Clear();
}
return(successfulStarts.Count);
}
public static long Solve()
{
int limit = 1000000;
EulerUtilities.LoadPrimes(limit);
bool[] isPrime = new bool[limit + 1];
long sum = 0;
foreach (long p in EulerUtilities.Primes)
{
isPrime[p] = true;
}
int m, factorial;
for (int i = 2; i <= limit; i++)
{
if (isPrime[i])
{
sum += i;
Console.WriteLine(i);
}
else
{
m = 2;
factorial = 1;
while (factorial != 0)
{
factorial = (factorial * m) % i;
m++;
}
sum += m - 1;
}
}
return(sum);
}
public static int Solve()
{
int count = 0, lychrelCount;
BigInteger number, reverse, result;
for (int n = 10; n < 10000; n++)
{
lychrelCount = 0;
number = n;
reverse = BigInteger.Parse(String.Concat(number.ToString().Reverse()));
result = number + reverse;
while (!EulerUtilities.IsPalindrome(result.ToString()) && lychrelCount < 50)
{
number = result;
reverse = BigInteger.Parse(String.Concat(number.ToString().Reverse()));
result = number + reverse;
lychrelCount++;
}
if (lychrelCount == 50)
{
count++;
}
}
return(count);
}
public static int Solve()
{
int compMinusTwoSquare = 0, square = 1;
int answer = 0;
bool found = false;
for (int composite = 35; composite < int.MaxValue && !found; composite += 2)
{
if (EulerUtilities.IsPrime(composite))
{
continue;
}
square = 1;
do
{
compMinusTwoSquare = composite - 2 * (int)Math.Pow(square, 2);
square++;
if (EulerUtilities.IsPrime(compMinusTwoSquare))
{
break;
}
} while(compMinusTwoSquare > 0);
if (compMinusTwoSquare < 0)
{
found = true;
answer = composite;
}
}
return(answer);
}
public static long Solve()
{
int limit = 10000000;
long sum = 0;
List <long> primes = EulerUtilities.GeneratePrimes(limit);
for (int p = 0; p < primes.Count; p++)
{
for (int q = p + 1; q < primes.Count; q++)
{
long pMul = primes[p];
long largest = 0;
if (primes[p] * primes[q] > limit)
{
break;
}
while (pMul * primes[q] <= limit)
{
long inter = pMul * primes[q];
while (inter <= limit)
{
if (inter > largest)
{
largest = inter;
}
inter *= primes[q];
}
pMul *= primes[p];
}
sum += largest;
}
}
return(sum);
}
private static void DrawCard(int[] deck, out int value)
{
value = deck[0];
for (int i = 0; i < deck.Length - 1; i++)
{
EulerUtilities.Swap(deck, i, i + 1);
}
}
public static Dictionary <int, Dictionary <int, int> > cache(int n)
{
var d = new Dictionary <int, Dictionary <int, int> >();
for (int i = 1; i <= n; i++)
{
d.Add(i, EulerUtilities.PrimeFactorsWithCount(i));
}
return(d);
}
public static long Solve()
{
long gcd = 13;
for (long n = 5; n <= Math.Pow(10, 3); n++)
{
Console.WriteLine((n - 1) + ": " + gcd + " | " + (double)gcd / (n - 1));
gcd += EulerUtilities.GreatestCommonDivisorBinary(gcd, n);
}
return(gcd);
}
public static long Solve()
{
List <long> primes = EulerUtilities.GeneratePrimes(2000000);
long sum = 0;
foreach (long prime in primes)
{
sum += prime;
}
return(sum);
}
public static int Solve(int low, int high)
{
int squareSums = (int)Math.Pow(EulerUtilities.SumRange(low, high), 2);
int sumSquares = 0;
for (int i = low; i <= high; i++)
{
sumSquares += (int)Math.Pow(i, 2);
}
return(squareSums - sumSquares);
}