def run():
for power in euler_util.numbers():
start = 10**power
cache = {}
for i in range(start, int(math.ceil(10**(power + 1) / 6.0))):
try:
try:
base_digs = cache[i]
except KeyError:
base_digs = euler_util.digits(i)
base_digs.sort()
cache[i] = base_digs
for x in range(2, 7):
val = x * i
try:
digs = cache[val]
except KeyError:
digs = euler_util.digits(val)
digs.sort()
cache[val] = digs
if not digs == base_digs:
raise Exc
print i
return
except Exc:
pass
def run():
primes = euler_util.GenFinder(euler_util.primes(9999))
for i in range(1000, 10000 - (3330 * 2)):
if not primes.contains(i):
continue
j = i + 3330
if not primes.contains(j):
continue
k = j + 3330
if not primes.contains(k):
continue
idigs = euler_util.digits(i)
idigs.sort()
jdigs = euler_util.digits(j)
jdigs.sort()
if not idigs == jdigs:
continue
kdigs = euler_util.digits(k)
kdigs.sort()
if not kdigs == idigs:
continue
match = [i, j, k]
match.sort()
print match
def is_lychrel(x):
digs = eu.digits(x)
for i in range(49):
rdigs = digs[:]
rdigs.reverse()
x += eu.undigits(rdigs)
digs = eu.digits(x)
if eu.palindrome(digs):
return False
return True
def curious(a,b):
if a % 10 == 0 and b % 10 == 0:
return False
a_digits = euler_util.digits(a)
b_digits = euler_util.digits(b)
for aidx in range(2):
for bidx in range(2):
if a_digits[aidx] == b_digits[bidx]:
if equiv(a,b,a_digits[alt(aidx)],b_digits[alt(bidx)]):
return True
return False
def run():
vals = []
for i in range(1000000):
if i == sum([d**5 for d in euler_util.digits(i)]):
vals.append(i)
print vals
print sum(vals) - 1
def run(target=8):
pgen = eu.GenFinder(eu.gen_primes())
# Loop over all prime numbers
for prime_idx in eu.numbers():
curr_prime = pgen[prime_idx]
curr_digits = eu.digits(curr_prime) # digits in current prime
# Get all selections of indices from current digits
for rindices in eu.selections(range(len(curr_digits))):
rzero = 0 in rindices
if len(rindices) == 0:
continue
found_primes = []
work_digs = curr_digits[:] # copy digits of current prime
# Choose the digit which we will insert at each index in rindices (the current selection)
for replacement in range(10):
if replacement == 0 and rzero:
continue
for rindex in rindices:
work_digs[rindex] = replacement
prime_idx = pgen.find(eu.undigits(work_digs))
if prime_idx != -1:
found_primes.append(pgen[prime_idx])
if len(found_primes) >= target:
# print "answer =",min(found_primes),found_primes,rindices
return min(found_primes)
def run():
data = {}
for i in range(1, 10000):
val = pow(i,3)
nval = eu.digits(val)
nval.sort()
nval.reverse()
nval = eu.undigits(nval)
try:
data[nval].append(val)
except KeyError:
data[nval] = [val]
min = None
for k,v in data.items():
if len(v) == 5:
if min is None or v[0] < min:
min = v[0]
return min
import euler_util
def complete(x):
y = x[:]
y.sort()
return y == range(1, 10)
max_val = 0
for digits in euler_util.permutations(range(1,10), 4):
base_value = euler_util.undigits(digits)
for i in euler_util.numbers(2):
curr_value = base_value * i
digits += euler_util.digits(curr_value)
if len(digits) > 9:
break
elif len(digits) == 9:
if complete(digits):
val = euler_util.undigits(digits)
# print base_value,i,val
if val > max_val:
max_val = val
break
# print max_val
def digital_sum(x):
return sum(eu.digits(x))
def test():
primes = [p for p in euler_util.primes(17)]
print curious(euler_util.digits(1406357289), primes)
def fact_sum(n):
digs = eu.digits(n)
return sum([math.factorial(x) for x in digs])
def run():
which_convergent = 100
cf = [cf_e(i) for i in range(which_convergent)]
b,c = convergent(cf)
print sum(eu.digits(b))
def curious(x):
d = eu.digits(x)
if len(d) == 1: return
return sum([eu.fact(i) for i in d]) == x
