def lychrel(n):
cnt = 0
while 1:
a = euler.intToSeq(n)
b = list(reversed(a))
a = euler.seqToInt(a)
b = euler.seqToInt(b)
n = a+b
if euler.palindrome(n):
return True
if cnt >50:
return False
cnt += 1
return True
def lychrel(n):
cnt = 0
while 1:
a = euler.intToSeq(n)
b = list(reversed(a))
a = euler.seqToInt(a)
b = euler.seqToInt(b)
n = a + b
if euler.palindrome(n):
return True
if cnt > 50:
return False
cnt += 1
return True
def getPrimes( dig, reploc ):
vals = [ combine(dig,reploc,repval) for repval in range(10) ]
# filter leading zeros
vals = [ v for v in vals if v != None ]
vals = [ euler.seqToInt(v) for v in vals ]
vals = [ v for v in vals if euler.isprime(v) ]
return vals
def getPrimes(dig, reploc):
vals = [combine(dig, reploc, repval) for repval in range(10)]
# filter leading zeros
vals = [v for v in vals if v != None]
vals = [euler.seqToInt(v) for v in vals]
vals = [v for v in vals if euler.isprime(v)]
return vals
def substringProps(seq):
lst = [(i, i + 3) for i in range(1, 8)]
div = [2, 3, 5, 7, 11, 13, 17]
for divisor, pair in zip(div, lst):
sub = seq[pair[0]:pair[1]]
val = euler.seqToInt(sub)
if val % divisor != 0:
return False
return True
def substringProps( seq ):
lst = [ (i,i+3) for i in range(1,8) ]
div = [2,3,5,7,11,13,17]
for divisor,pair in zip(div,lst):
sub = seq[pair[0]:pair[1]]
val = euler.seqToInt( sub )
if val % divisor != 0:
return False
return True
def increasingIter(minv,digits):
def impl(minv,digits):
if digits == 0:
yield []
else:
for i in [0] + range(minv,10):
for j in impl(i,digits-1):
yield [i] + j
for i in impl(minv,digits):
yield euler.seqToInt(i)
def increasingIter(minv, digits):
def impl(minv, digits):
if digits == 0:
yield []
else:
for i in [0] + range(minv, 10):
for j in impl(i, digits - 1):
yield [i] + j
for i in impl(minv, digits):
yield euler.seqToInt(i)
import euler
for i in range(9):
print '----'
lst = range(1, i + 2)
lst.reverse()
for perm in euler.permutations(lst):
v = euler.seqToInt(perm)
if euler.isprime(v):
print v
break
def concatPrimes(a,b):
astr = euler.intToSeq(a)
bstr = euler.intToSeq(b)
return euler.seqToInt(astr+bstr)
def test(n):
maxperm = euler.seqToInt(max_perm(n**3))
y = int( math.ceil( maxperm**(1./3) ) )
return y
res.append(s)
return res
def validPandigital():
for a in foo(2):
for b in foo(7):
for c in foo(17):
s = set(a+b+c)
if len(s) == 9:
last = list(set(range(10)) - s)[0]
x = [last] + a + b + c
yield x
def substringProps( seq ):
lst = [ (i,i+3) for i in range(1,8) ]
div = [2,3,5,7,11,13,17]
for divisor,pair in zip(div,lst):
sub = seq[pair[0]:pair[1]]
val = euler.seqToInt( sub )
if val % divisor != 0:
return False
return True
res = []
for x in validPandigital():
if substringProps(x):
print x
res.append( euler.seqToInt(x) )
print 'soln',sum(res)
import euler
for i in range(9):
print '----'
lst = range(1,i+2)
lst.reverse()
for perm in euler.permutations(lst):
v = euler.seqToInt(perm)
if euler.isprime(v):
print v
break
def concatPrimes(a, b):
astr = euler.intToSeq(a)
bstr = euler.intToSeq(b)
return euler.seqToInt(astr + bstr)
yield [i] + j
for i in impl(minv,digits):
yield euler.seqToInt(i)
res = []
for i in set(increasingIter(0,6)):
fc = factorialChain(i)
fcl = len(fc)-1
if fcl == 60:
res.append( i )
final = []
for r in res:
s = set()
for p in euler.permutations(euler.intToSeq(r)):
v = euler.seqToInt(p)
if factorialChainLength(v) == 60:
s.add(v)
for item in s:
final.append(item)
cnt = 0
final = list(set(final))
final.sort()
for item in final:
cnt += 1
print cnt,item,factorialChainLength(item)
print 'soln',cnt
def tleft(n):
seq = euler.intToSeq(n)
return [seq[:i] for i in range(1, len(seq) + 1)]
def tright(n):
seq = euler.intToSeq(n)
return [seq[i:] for i in range(0, len(seq))]
def tall(n):
return tleft(n) + tright(n)
res = []
for n in euler.sieve(4000):
if n > 7:
seq = tall(n)
seq = [euler.seqToInt(x) for x in seq]
seq = [euler.isprime(x) for x in seq]
val = reduce(lambda a, b: a and b, seq, True)
if val:
res.append(n)
print n, seq
print 'soln', sum(res) + 739397
#if sum([ 1 for x in seq if not euler.isprime(x) ]) == 0:
# print n
import euler
def tleft(n):
seq = euler.intToSeq(n)
return [ seq[:i] for i in range(1,len(seq)+1) ]
def tright(n):
seq = euler.intToSeq(n)
return [ seq[i:] for i in range(0,len(seq)) ]
def tall(n):
return tleft(n) + tright(n)
res = []
for n in euler.sieve(4000):
if n > 7:
seq = tall(n)
seq = [ euler.seqToInt(x) for x in seq ]
seq = [ euler.isprime(x) for x in seq ]
val = reduce( lambda a,b : a and b, seq, True )
if val:
res.append(n)
print n,seq
print 'soln',sum(res) + 739397
#if sum([ 1 for x in seq if not euler.isprime(x) ]) == 0:
# print n
import euler
def generate(n):
res = []
c = 1
while len(res) < 9:
res += euler.intToSeq(n*c)
c+=1
if len(res) == 9:
return res
return None
def isPandigital(seq):
return len(seq) == len(set(seq)) and (0 not in seq)
res = []
for i in range(1,10000):
x = generate(i)
if x != None:
if isPandigital(x):
res.append(euler.seqToInt(x))
print i,x
res.sort()
print res
for i in impl(minv, digits):
yield euler.seqToInt(i)
res = []
for i in set(increasingIter(0, 6)):
fc = factorialChain(i)
fcl = len(fc) - 1
if fcl == 60:
res.append(i)
final = []
for r in res:
s = set()
for p in euler.permutations(euler.intToSeq(r)):
v = euler.seqToInt(p)
if factorialChainLength(v) == 60:
s.add(v)
for item in s:
final.append(item)
cnt = 0
final = list(set(final))
final.sort()
for item in final:
cnt += 1
print cnt, item, factorialChainLength(item)
print 'soln', cnt
