def potential_truncatable_primes():
begin_digits = (2,3,4,5,7)
middle_digits = (1,3,7,9)
end_digits = (3,7)
for i in count():
for num in [ render_to_number(seq) for seq in
[ (beg,) + mid + (end,)
for beg in begin_digits
for mid in product(middle_digits, repeat=i)
for end in end_digits
] ]:
yield num
def pandigitals(length):
if length > 10:
raise Exception('Pandigital number cannot be longer than 10 digits.')
if length < 10:
digits = range(1,length+1)
else:
digits = range(length)
for perm in ifilter(lambda x: x[0] != 0, permutations(digits)):
if perm[0] == 0: continue
yield render_to_number(perm)
def pandigital_concat_products():
start_set = set(range(1,10))
for i in xrange(1,100000):
remaining = start_set.copy()
seq = []
for n in xrange(1,10):
product = i * n
product_list = [ int(digit) for digit in str(product) ]
product_set = set(product_list)
if len(product_list) != len(product_set):
break
if product_set <= remaining:
remaining -= product_set
seq += product_list
else:
break
if len(remaining) == 0:
yield (i, render_to_number(seq))
break