def main():
v = fraction.Fraction(1, 2)
cnt = 0
for i in range(1, 1000):
v = contFraction(v)
v = v.cancel()
r = v + fraction.Fraction(1, 1)
numseq = euler.intToSeq(r.num)
denseq = euler.intToSeq(r.den)
if len(numseq) > len(denseq):
print i + 1
cnt += 1
print 'soln', cnt
def main():
v = fraction.Fraction(1,2)
cnt = 0
for i in range(1,1000):
v = contFraction(v)
v = v.cancel()
r = v+fraction.Fraction(1,1)
numseq = euler.intToSeq(r.num)
denseq = euler.intToSeq(r.den)
if len(numseq) > len(denseq):
print i+1
cnt += 1
print 'soln',cnt
def nDigitGen(n):
lb,ub = bounds(n)
res = []
for i in range(lb,ub+1):
if len(euler.intToSeq(i**n)) == n:
res.append( (i,i**n) )
return res
def nDigitGen(n):
lb, ub = bounds(n)
res = []
for i in range(lb, ub + 1):
if len(euler.intToSeq(i**n)) == n:
res.append((i, i**n))
return res
def valid(i):
lst = [(-3,9),(-5,8),(-7,7),(-9,6),(-11,5),(-13,4)]
#lst = [(-3,9),(-5,8),,(-11,5),(-13,4)]
seq = euler.intToSeq(i)
for a,b in lst:
if seq[a] != b:
return False
return True
def valid(i):
lst = [(-3, 9), (-5, 8), (-7, 7), (-9, 6), (-11, 5), (-13, 4)]
#lst = [(-3,9),(-5,8),,(-11,5),(-13,4)]
seq = euler.intToSeq(i)
for a, b in lst:
if seq[a] != b:
return False
return True
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 combine( dig, reploc, repval ):
digseq = euler.intToSeq(dig)
seqn = len(digseq) + len(reploc)
j = 0
res = [ None for i in range(seqn) ]
for i in range(seqn):
if i in reploc:
res[i] = repval
else:
res[i] = digseq[j]
j += 1
if res[0] == 0:
return None
return res
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 combine(dig, reploc, repval):
digseq = euler.intToSeq(dig)
seqn = len(digseq) + len(reploc)
j = 0
res = [None for i in range(seqn)]
for i in range(seqn):
if i in reploc:
res[i] = repval
else:
res[i] = digseq[j]
j += 1
if res[0] == 0:
return None
return res
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 ndigits(x):
return len(euler.intToSeq(x))
def test_decreasing(self):
self.assert_( isDecreasing(euler.intToSeq(134468))==False )
self.assert_( isDecreasing(euler.intToSeq(66420))==True )
self.assert_( isDecreasing(euler.intToSeq(155349))==False )
import euler
import math
def isPandigital(seq):
a = set(seq).intersection(set(range(1,10)))
return len(a) == 9
def fibiter():
a = 0
b = 1
yield a
while 1:
yield b
a, b = b, a+b
for i,v in enumerate(fibiter()):#xrange(2,100000):
if isPandigital(euler.intToSeq(v % 10**9)):
v2 = v / 10**(int(math.ceil(math.log10(v)))-11)
v2 = euler.intToSeq(v2)[:9]
print i
if isPandigital(v2):
break
def isPerm(a, b):
return set(euler.intToSeq(a)) == set(euler.intToSeq(b))
import euler
import math
def isPandigital(seq):
a = set(seq).intersection(set(range(1, 10)))
return len(a) == 9
def fibiter():
a = 0
b = 1
yield a
while 1:
yield b
a, b = b, a + b
for i, v in enumerate(fibiter()): #xrange(2,100000):
if isPandigital(euler.intToSeq(v % 10**9)):
v2 = v / 10**(int(math.ceil(math.log10(v))) - 11)
v2 = euler.intToSeq(v2)[:9]
print i
if isPandigital(v2):
break
def relevant(i):
a = euler.intToSeq(i)
a.sort()
b = euler.intToSeq(phi[i])
b.sort()
return a == b
def max_perm(n):
seq = euler.intToSeq(n)
seq.sort()
seq.reverse()
return seq
def tright(n):
seq = euler.intToSeq(n)
return [seq[i:] for i in range(0, len(seq))]
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 tleft(n):
seq = euler.intToSeq(n)
return [ seq[:i] for i in range(1,len(seq)+1) ]
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 numberChainNext(n):
seq = euler.intToSeq(n)
seq = [i * i for i in seq]
return sum(seq)
def isBouncy(n):
seq = euler.intToSeq(n)
return (not isIncreasing(seq)) and (not isDecreasing(seq))
def isPerm( a, b ):
return set( euler.intToSeq(a) ) == set( euler.intToSeq(b) )
import euler
res = []
for a in range(2,100):
for b in range(2,100):
v = sum(euler.intToSeq(a**b))
res.append(v)
print max(res)
# res.append([ sum(euler.intToSeq(2**b)) for b in range(100) ]))
#print max(res)
def test_decreasing(self):
self.assert_(isDecreasing(euler.intToSeq(134468)) == False)
self.assert_(isDecreasing(euler.intToSeq(66420)) == True)
self.assert_(isDecreasing(euler.intToSeq(155349)) == False)
def concatPrimes(a,b):
astr = euler.intToSeq(a)
bstr = euler.intToSeq(b)
return euler.seqToInt(astr+bstr)
def concatPrimes(a, b):
astr = euler.intToSeq(a)
bstr = euler.intToSeq(b)
return euler.seqToInt(astr + bstr)
def numberChainNext(n):
seq = euler.intToSeq(n)
seq = [ i*i for i in seq ]
return sum(seq)
def relevant(i):
a = euler.intToSeq(i)
a.sort()
b = euler.intToSeq(phi[i])
b.sort()
return a==b
for j in impl(i,digits-1):
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 factorialChainNext(n):
seq = euler.intToSeq(n)
seq = [f[i] for i in seq]
return sum(seq)
def factorialChainNext(n):
seq = euler.intToSeq(n)
seq = [ f[i] for i in seq ]
return sum(seq)
def isBouncy(n):
seq = euler.intToSeq(n)
return (not isIncreasing(seq)) and (not isDecreasing(seq))
