def run(exp):
st = str(2**exp); #Raise 2 to exp power and make a string of the number.
m = map(int, st); #Turn digits into integers.
s = sum(m); #Sum them.
#Report completion.
eulersupport.write_output(s);
def run():
#Get the input file.
f = eulersupport.get_input_file()
#Initialize the matrix.
matrix = []
for l in f.readlines():
l = l.replace("\n", "")
matrix.append(map(int, l.split(" ")))
greatest = -1
#Perform the calculations.
for i in xrange(len(matrix)):
for j in xrange(len(matrix[i])):
h = find_horizontal(matrix, i, j)
v = find_vertical(matrix, i, j)
d1 = find_diagonal1(matrix, i, j)
d2 = find_diagonal2(matrix, i, j)
curr = max([h, v, d1, d2])
if (curr > greatest):
greatest = curr
#Print the results.
eulersupport.write_output(greatest)
def run():
#Get the input file.
f = eulersupport.get_input_file();
#Initialize the matrix.
matrix = [];
for l in f.readlines():
l = l.replace("\n", "");
matrix.append(map(int, l.split(" ")));
greatest = -1;
#Perform the calculations.
for i in xrange(len(matrix)):
for j in xrange(len(matrix[i])):
h = find_horizontal(matrix, i, j);
v = find_vertical(matrix, i, j);
d1 = find_diagonal1(matrix, i, j);
d2 = find_diagonal2(matrix, i, j);
curr = max([h,v,d1,d2]);
if(curr > greatest):
greatest = curr;
#Print the results.
eulersupport.write_output(greatest);
def run(upperbound):
number = str(
sum(map(pow, xrange(1, upperbound + 1), xrange(1, upperbound + 1))))
result = number[-10:]
#Report Completion.
eulersupport.write_output(result)
def run():
lines = eulersupport.get_input_file().readlines(); #List of numbers as Strings.
m = map(int, lines); #Map the numbers into ints.
nstr = str(sum(m)); #Sum them and transform it into a string.
snstr = nstr[:10]; #Get the first 10 digits.
#Report completion.
eulersupport.write_output(snstr);
def run():
prime = (28433) * (2**7830457) + 1
#Extract the last 10 digits of the number.
prime_str = str(prime)
last_ten = prime_str[len(prime_str) - 10:len(prime_str)]
#Report Completion.
eulersupport.write_output(last_ten)
def run(upperbound):
result = -1
factors = eulermath.prime_factors(upperbound)
for factor in factors:
if (factor[0] > result):
result = factor[0]
eulersupport.write_output(result)
def run(upperbound):
result = -1;
factors = eulermath.prime_factors(upperbound);
for factor in factors:
if(factor[0] > result):
result = factor[0];
eulersupport.write_output(result);
def run():
prime = (28433) * (2**7830457) + 1
#Extract the last 10 digits of the number.
prime_str = str(prime);
last_ten = prime_str[len(prime_str)-10 : len(prime_str)];
#Report Completion.
eulersupport.write_output(last_ten);
def run():
result = 0;
for i in range(0, 1000000):
if(is_palindrome_2(i) and eulermath.is_palindrome(i)):
print i;
result += i;
#Print the result.
eulersupport.write_output(result);
def run():
result = 0
for i in range(0, 1000000):
if (is_palindrome_2(i) and eulermath.is_palindrome(i)):
print i
result += i
#Print the result.
eulersupport.write_output(result)
def run(upperbound):
result = 0; #Sum of all values evenly divisible by 5 and 3.
for i in range(1, upperbound):
#Is evenly divisible by the two numbers?
if((i % 3 == 0) or (i % 5 == 0)):
result += i;
#Report Completion.
eulersupport.write_output(result);
def run(upperbound):
helper = eulermath.PrimesHelper();
print "Starting find primes...";
helper.find_all_primes_up_to_n(upperbound);
print "Find primes done."
result = sum(helper.get_primes());
#Report completion.
eulersupport.write_output(result);
def run(upperbound):
helper = eulermath.PrimesHelper()
print "Starting find primes..."
helper.find_all_primes_up_to_n(upperbound)
print "Find primes done."
result = sum(helper.get_primes())
#Report completion.
eulersupport.write_output(result)
def run():
#Find all numbers.
find_all_abundant_numbers()
#Sum of all numbers that cannot be writton.
result = find_sum_cannot_be_written()
#Report completion.
eulersupport.write_output(result)
def run():
result = -1;
for i in eulermath.infinite_range(9, 2):
if(not f(i)):
result = i;
break;
print result;
#Report Completion.
eulersupport.write_output(result);
def run(upperbound):
numbers = range(1, upperbound + 1); #All numbers up to upperbound.
sum_of_squares = sum(map(pow, numbers, [2] * (upperbound)));
square_of_sums = sum(numbers) ** 2;
result = (square_of_sums - sum_of_squares);
#Report completion.
eulersupport.write_output(result);
def run():
result = -1
for i in eulermath.infinite_range(9, 2):
if (not f(i)):
result = i
break
print result
#Report Completion.
eulersupport.write_output(result)
def run():
count = 0;
for n in xrange(1, 100 + 1):
for r in range(1, n+1):
a = nCr(n,r);
if(a > 1000000):
count += 1;
#Print the result.
eulersupport.write_output(count);
def run(upperbound):
s = 0; #Sum of all amicable numbers.
for i in xrange(1, upperbound +1):
# print i;
if(eulermath.is_amicable(i)):
eulersupport.log(i, "is amicable.");
s += i;
#Report completion.
eulersupport.write_output(s);
def run(upperbound):
result = 0
#Sum of all values evenly divisible by 5 and 3.
for i in range(1, upperbound):
#Is evenly divisible by the two numbers?
if ((i % 3 == 0) or (i % 5 == 0)):
result += i
#Report Completion.
eulersupport.write_output(result)
def run(upperbound):
#calculate the factorial of the number.
f = eulermath.factorial(upperbound)
#First turn the number into a string, next for each char turn it into a
#int and return a list of the digits contained at number.
m = map(int, str(f))
#Sum all digits of number.
s = sum(m)
#Report completion.
eulersupport.write_output(s)
def run(upperbound):
s = 0
#Sum of all amicable numbers.
for i in xrange(1, upperbound + 1):
# print i;
if (eulermath.is_amicable(i)):
eulersupport.log(i, "is amicable.")
s += i
#Report completion.
eulersupport.write_output(s)
def run():
result = 0
for i in eulermath.permutations(list("1234567890")):
str_i = eulersupport.list_to_str(i)
int_i = int(str_i)
if (eulermath.is_strictly_pandigital(int_i, 0, 9) and f(int_i)):
print str_i
result += 1
eulersupport.write_output(result)
def run():
result = 0;
for i in eulermath.permutations(list("1234567890")):
str_i = eulersupport.list_to_str(i);
int_i = int(str_i);
if(eulermath.is_strictly_pandigital(int_i, 0, 9) and f(int_i)):
print str_i;
result += 1;
eulersupport.write_output(result);
def run():
maximum = 0
for a in xrange(1, 100):
for b in xrange(1, 100):
print a, b
curr_sum = sum(map(int, str(pow(a, b))))
if (curr_sum > maximum):
maximum = curr_sum
#Report Completion.
eulersupport.write_output(maximum)
def run(upperbound):
#calculate the factorial of the number.
f = eulermath.factorial(upperbound);
#First turn the number into a string, next for each char turn it into a
#int and return a list of the digits contained at number.
m = map(int, str(f));
#Sum all digits of number.
s = sum(m);
#Report completion.
eulersupport.write_output(s);
def run(upperbound):
for m in xrange(1, 1000):
for n in xrange(1, m):
a = 2 * m * n
b = m**2 - n**2
c = m**2 + n**2
#Is the triplet the we wants?
if (a + b + c == upperbound):
#Report Completion
eulersupport.write_output(a * b * c)
return
def run(upperbound):
for m in xrange(1, 1000):
for n in xrange(1, m):
a = 2*m*n;
b = m**2 - n**2;
c = m**2 + n**2;
#Is the triplet the we wants?
if(a + b + c == upperbound):
#Report Completion
eulersupport.write_output(a * b * c);
return; #Go out we are done.
def run():
maximum = 0;
for a in xrange(1, 100):
for b in xrange(1, 100):
print a, b;
curr_sum = sum(map(int, str(pow(a,b))));
if(curr_sum > maximum):
maximum = curr_sum;
#Report Completion.
eulersupport.write_output(maximum);
def run():
lines = eulersupport.get_input_file().readlines()
#List of numbers as Strings.
m = map(int, lines)
#Map the numbers into ints.
nstr = str(sum(m))
#Sum them and transform it into a string.
snstr = nstr[:10]
#Get the first 10 digits.
#Report completion.
eulersupport.write_output(snstr)
def run(upperbound):
result = 0; #Sum of even-valued elements.
for n in eulermath.fibonacci(1, 2):
#if is even add it to result.
if(n % 2 == 0):
result += n;
if(n > upperbound):
break;
#Report Completion.
eulersupport.write_output(result);
def run():
for j in eulermath.infinite_range(1):
Pj = eulermath.pentagonal_number(j);
for k in xrange(1, j):
Pk = eulermath.pentagonal_number(k);
s = Pj + Pk;
d = Pj - Pk;
if(eulermath.is_pentagonal_number(s) and eulermath.is_pentagonal_number(d)):
eulersupport.write_output(d);
return;
def run(p):
result = 0;
index = 2;
upper_bound = int("9" * (p+1));
while(index < upper_bound):
if(f(index, p)):
result += index;
index += 1;
#Print the result.
eulersupport.write_output(result);
def run(lowerbound, upperbound):
a = lowerbound; #Base
b = upperbound; #Exp
l = set(); #All distinct terms.
for i in range(lowerbound, upperbound+1):
for j in range(lowerbound, upperbound+1):
n = i ** j;
l.add(n);
#Report completion.
eulersupport.write_output(len(l));
def run():
eulermath.PrimesHelper().find_all_primes_up_to_n(7)
list_of_primes = []
while len(list_of_primes) != 11:
prime = eulermath.PrimesHelper().find_next_prime()
if fr(prime) and fl(prime):
list_of_primes.append(prime)
print list_of_primes
result = sum(list_of_primes)
eulersupport.write_output(result)
def run(p):
result = 0
index = 2
upper_bound = int("9" * (p + 1))
while (index < upper_bound):
if (f(index, p)):
result += index
index += 1
#Print the result.
eulersupport.write_output(result)
def run():
for j in eulermath.infinite_range(1):
Pj = eulermath.pentagonal_number(j)
for k in xrange(1, j):
Pk = eulermath.pentagonal_number(k)
s = Pj + Pk
d = Pj - Pk
if eulermath.is_pentagonal_number(s) and eulermath.is_pentagonal_number(d):
eulersupport.write_output(d)
return
def run(upperbound):
count_89 = 0;
count_1 = 0;
count_other = 0;
for i in xrange(0, upperbound):
chain = find_chain(i);
if (chain[0] == 89): count_89 += 1;
elif(chain[0] == 1): count_1 += 1;
#Report Completion.
eulersupport.write_output(count_89);
def run():
m = map(str, range(1, 1000001)); #Create the fraction.
s = str().join(m); #Turn it into one string.
prod = 1;
for pwr in xrange(0,7): #iterate for the power
index = pow(10, pwr); #Calculate the index.
digit = int(s[index -1]); #Get the digit.
print index, digit
prod *= digit ;
#Print the result.
eulersupport.write_output(prod);
def run(upperbound):
count_89 = 0
count_1 = 0
count_other = 0
for i in xrange(0, upperbound):
chain = find_chain(i)
if (chain[0] == 89): count_89 += 1
elif (chain[0] == 1): count_1 += 1
#Report Completion.
eulersupport.write_output(count_89)
def run(upperbound):
size = 0; #How many digits the element has.
index = 0; #Index of the target number in the fibonacci sequence.
for n in eulermath.fibonacci(1, 1):
size = len(str(n));
index += 1;
if(size == upperbound):
break;
#Report completion.
eulersupport.write_output(index);
def run(upperbound):
result = 0
#Sum of even-valued elements.
for n in eulermath.fibonacci(1, 2):
#if is even add it to result.
if (n % 2 == 0):
result += n
if (n > upperbound):
break
#Report Completion.
eulersupport.write_output(result)
def run(upperbound):
l = [];
for i in range(1, upperbound + 1):
list_of_results = f(i); #Get the results for the i.
if(len(list_of_results) != 0):
print i, list_of_results;
l += [[len(list_of_results), i]];
l.sort();
#Print the result.
eulersupport.write_output(l[-1]);
def run(upperbound):
maxSize = 0; #Greatest sequence.
n = 0; #The number the produces the greatest sequence.
for i in range(1, upperbound + 1):
print i;
size = collatz(i); #Get the size of the sequence.
if(size > maxSize):
maxSize = size;
n = i;
#Print the result.
eulersupport.write_output(n);
def run(exp):
max_value = (10 ** exp) -1; #Inclusive upper bound of values.
max_palin = 0; #Greater palindrome found.
#Search backwards.
for i in range(max_value, 1, -1):
for j in range(i, 1, -1):
#The number is palindrome and is greater that
#current max palindrome?
if((i * j) > max_palin and eulermath.is_palindrome(i * j)):
max_palin = (i * j);
#Print the result.
eulersupport.write_output(max_palin);
def run(upperbound):
l = []
for i in range(1, upperbound + 1):
list_of_results = f(i)
#Get the results for the i.
if (len(list_of_results) != 0):
print i, list_of_results
l += [[len(list_of_results), i]]
l.sort()
#Print the result.
eulersupport.write_output(l[-1])
def run(upperbound):
size = 0
#How many digits the element has.
index = 0
#Index of the target number in the fibonacci sequence.
for n in eulermath.fibonacci(1, 1):
size = len(str(n))
index += 1
if (size == upperbound):
break
#Report completion.
eulersupport.write_output(index)
def run(upperbound):
maxSize = 0
#Greatest sequence.
n = 0
#The number the produces the greatest sequence.
for i in range(1, upperbound + 1):
print i
size = collatz(i)
#Get the size of the sequence.
if (size > maxSize):
maxSize = size
n = i
#Print the result.
eulersupport.write_output(n)
def run(upperbound):
result = 0;
i = 1;
while(True):
n = eulermath.triangle_number(i);
count = eulermath.factors_count(n);
eulersupport.log(n, count);
if(count > upperbound):
result = n;
break;
i += 1;
#Report Completion.
eulersupport.write_output(result);
def run():
index = 3
result = 0
while (index < 10**7):
list_d = eulermath.list_of_digits(index)
list_factorial_d = map(eulermath.factorial, list_d)
sum_of_factorials = sum(list_factorial_d)
if (sum_of_factorials == index):
print index
result += index
index += 1
# Print the result.
eulersupport.write_output(result)
def run():
upper_bound = 10000
count = 0
for i in xrange(1, upper_bound):
for exp in xrange(1, upper_bound):
n = i**exp
digits = len(str(n))
print "exp: " + str(exp)
print "digits: " + str(digits)
if (digits == exp):
print str(i) + "**" + str(exp) + " = " + str(n)
count += 1
elif (digits > exp):
break
#Report Completion.
eulersupport.write_output(count)
def run(upperbound):
list_of_primes = [];
#Find all the primes.
eulermath.PrimesHelper().find_all_primes_up_to_n(upperbound);
for prime in eulermath.PrimesHelper().get_primes():
digits = list(str(prime));
#Check if all permutations are prime.
perms = eulermath.all_rotations(digits);
perms = [int(eulersupport.list_to_str(perm)) for perm in perms];
all_perms_are_prime = all(eulermath.PrimesHelper().is_prime(x) for x in perms);
print prime, "-", perms, all_perms_are_prime;
#Add to list of primes
if(all_perms_are_prime):
list_of_primes.append(prime);
eulersupport.write_output(len(list_of_primes));
def run(lowerbound, upperbound):
result = {
"a": 0,
"b": 0,
"count": 0
}
#Try all formulas.
for a in xrange(lowerbound + 1, upperbound):
for b in xrange(lowerbound + 1, upperbound):
count = countPrimes(a, b)
if (count != 0):
if (count > result["count"]):
result["a"] = a
result["b"] = b
result["count"] = count
print result
eulersupport.write_output(result["a"] * result["b"])
def run():
factors_count = 4
consecutive_count = 4
consecutive_list = []
result = None
for i in eulermath.infinite_range(0):
print i
factors = eulermath.prime_factors(i)
if (len(factors) == factors_count):
consecutive_list.append(i)
else:
consecutive_list = []
if (len(consecutive_list) == consecutive_count):
result = consecutive_list[0]
break
eulersupport.write_output(result)
def run():
list_of_pandigitals = [];
upperbound = 999999 + 1;
for a in xrange(2, upperbound):
for b in xrange(2, a):
#Create a concatenated product of a by (1...n)
con_prod = concatenated_product(a, b);
#We reach a number that is bigger than 9 digits.
#has no meaning to keeping searching because it'll not
#be a pandigital number.
if(len(con_prod) > 9): break;
if(eulermath.is_strictly_pandigital(con_prod, 1, 9)):
list_of_pandigitals += [con_prod];
list_of_pandigitals.sort();
result = list_of_pandigitals[len(list_of_pandigitals)-1];
#Print the result.
eulersupport.write_output(result);
