def is_trunc(n):
if not euler.is_prime(n):
return False
d = euler.digits(n)
for c in range(1,len(d)):
lt = euler.num_from_digits(d[:-c])
rt = euler.num_from_digits(d[c:])
if not (euler.is_prime(lt) and euler.is_prime(rt)):
return False
return True
def has_div(d, os, denom):
s = 9 - os
if denom == 2:
return d[s - 2] & 1 == 0
if denom == 3:
return sum(d[s:s - 3:-1]) % 3 == 0
if denom == 5:
return d[s - 2] == 5 or d[s - 2] == 0
return euler.num_from_digits(d[s - 2:s + 1]) % denom == 0
def is_pand_multiple(n):
for f in range(1,5):
nd = euler.digits(n)
basen = euler.num_from_digits(nd[-f:])
currn = basen
nd = nd[:-f]
while nd:
currn += basen
cnd = euler.digits(currn)
if (nd[-len(cnd):] != cnd):
break
nd = nd[:-len(cnd)]
if not nd:
return True
return False
#!/usr/bin/python
import euler
import math
def is_pand_multiple(n):
for f in range(1,5):
nd = euler.digits(n)
basen = euler.num_from_digits(nd[-f:])
currn = basen
nd = nd[:-f]
while nd:
currn += basen
cnd = euler.digits(currn)
if (nd[-len(cnd):] != cnd):
break
nd = nd[:-len(cnd)]
if not nd:
return True
return False
for p in euler.perms(list(reversed(range(1,10))), rev=True):
n = euler.num_from_digits(reversed(p))
if (is_pand_multiple(n)):
print(n)
break
primes = euler.sieve(UpTo)
circular = [0] * len(primes)
def rotate(d):
return d[-1:] + d[:-1]
for x in range(0, len(primes)):
if not primes[x]:
continue
if circular[x]:
continue
d = rotate(euler.digits(x))
rd = euler.num_from_digits(d)
while rd != x:
if not primes[rd]:
break
d = rotate(d)
rd = euler.num_from_digits(d)
if rd == x:
d = rotate(d)
rd = euler.num_from_digits(d)
circular[x] = 1
while rd != x:
circular[rd] = 1
d = rotate(d)
rd = euler.num_from_digits(d)
import euler
def has_div(d, os, denom):
s = 9 - os
if denom == 2:
return d[s - 2] & 1 == 0
if denom == 3:
return sum(d[s:s - 3:-1]) % 3 == 0
if denom == 5:
return d[s - 2] == 5 or d[s - 2] == 0
return euler.num_from_digits(d[s - 2:s + 1]) % denom == 0
def has_property(d):
return (has_div(d, 1, 2) and has_div(d, 2, 3) and has_div(d, 3, 5)
and has_div(d, 4, 7) and has_div(d, 5, 11) and has_div(d, 6, 13)
and has_div(d, 7, 17))
digits = range(10)
Valid = []
while digits:
if (has_property(digits)):
Valid.append(euler.num_from_digits(digits))
digits = euler.next_perm(digits)
print(Valid)
print(sum(Valid))