def checkperm(x,y):
xa = int2array(x)
ya = int2array(y)
isperm = True
for elem in xa:
if elem in ya:
ya.pop(ya.index(elem))
else:
isperm = False
break
return isperm
def checkdigits(t):
check = 0
ar = int2array(t[0])
br = int2array(t[1])
ar.sort()
br.sort()
if len(ar) == len(br):
for ii in range(len(ar)):
if ar[ii] != br[ii]:
break
if ii == len(ar)-1:
check = 1
return check
def replaceprime(prime):
findall = lambda my_list: [i for i, x in enumerate(my_list) if x == '1']
ndig = len(int2array(prime))
pgroup = []
replacement_dig = make_palindrome_half(ndig-1)
# Ignore the last replacement rule, it is '0000'
for reprule in replacement_dig[:-1]:
# Run replacement for all integers
subgroup = []
newprime = int2array(prime)
for cint in range(10):
for ind in findall(reprule):
newprime[ind] = cint
# Check that the length is the same
if len(newprime) == len(int2array(array2int(newprime))):
subgroup.append(array2int(newprime))
pgroup.append(subgroup)
return pgroup
from eulermath import int2array
if __name__ = "__main__":
# nexp = 15 # Test case, should give 26
nexp = 1000
print "The sum of the digits in 2^", nexp, "is:", sum(int2array(2**nexp))
import math
from eulermath import int2array
# Applies the factorial to each element in a list
def facArray(arr):
newarr = []
for i in arr:
newarr.append(math.factorial(i))
return newarr
if __name__ == "__main__":
# Find the upper bound we need to go to
for ii in range(2, 10):
ninestr = int("9"*ii)
ninetotal = sum(facArray(int2array(ninestr)))
if (ninetotal < ninestr):
print "max bound = ", ninestr
nmax = ninestr
break
totalsum = 0
n = 3
while (n < nmax):
intarr = int2array(n)
intsum = sum(facArray(intarr))
if intsum == n:
print intsum
totalsum += intsum
n += 1
import math
from eulermath import int2array
if __name__ == "__main__":
# n = 10 # Test case, should give 27
n = 100
# print math.factorial(n)
myarray = int2array(math.factorial(n))
sumdigits = 0
# print myarray
for x in myarray:
sumdigits += x
print "The sum of the digits of", (str(n)+"!"), "is:", sumdigits
def truncateRL(num):
arr = int2array(num)
arr.pop()
tnum = array2int(arr)
return tnum
# Find the one other sequence of 4-digit permuted increasing primes
# The first is; 1487, 4817, 8147 (difference is 3330)
from eulermath import (isprime, int2array, array2int,
find_primes_in_list, find_arithemetric_series)
from itertools import permutations, combinations
if __name__ == "__main__":
# Start by finding all 4-digit primes
print "Finding arithemetric series of primes between 1001 and 9999:"
exclude = []
for trial in xrange(1001, 9999, 2):
if trial not in exclude:
if isprime(trial):
# Find the permutations of this number
tp = permutations(int2array(trial))
# Get the unique values and sort them
tpl = list(set([array2int(x) for x in tp]))
tpp = find_primes_in_list(tpl)
tpn = []
for x in tpp:
if x > 1000:
tpn.append(x)
# Exclude the others
for p in tpn:
exclude.append(p)
# Find any arithemetric series of length 3 in the prime list
aseries = find_arithemetric_series(tpn, 3)
if len(aseries) > 0:
print aseries
for series in aseries:
print series
def nextterm(n):
return sum(map(factorial, int2array(n)))
tsublist.append(slist[ii])
trimmed.append(tsublist)
return trimmed
if __name__ == "__main__":
# Import the data
sub = []
p123 = []
p12 = []
p23 = []
p1 = []
p2 = []
p3 = []
fnames = open('Euler79.dat')
for line in fnames:
val = int2array(int(line))
# All values
sub.append(val)
# Single values
p1.append(val[0])
p2.append(val[1])
p3.append(val[2])
# Pairs
p12.append(array2int(val[0:2]))
p23.append(array2int(val[1:3]))
p123.append(array2int(val))
# Flatten out the sublist and take all unique elements
fsl = list(set([x for arr in sub for x in arr]))
# this length is the shortest password size
def haslongnum(frac):
ln = 0
if len(int2array(frac.numerator)) > len(int2array(frac.denominator)):
ln = 1
return ln
# Applies the power operator to each element in a list
def powArray(arr, mypow):
newarr = []
for i in arr:
newarr.append(i**mypow)
return newarr
if __name__ == "__main__":
# npow = 4 #Test case, should give 19316 = 1634 + 8208 + 9474
npow = 5
# nmax = 10**6 # Old upper bound, set arbitrarially
# Find the upper bound we need to go to
for ii in range(2, 10):
ninestr = int("9"*ii)
ninetotal = sum(powArray(int2array(ninestr), npow))
if (ninetotal < ninestr):
print "max bound = ", ninestr
nmax = ninestr
break
totalsum = 0
n = 2
while (n < nmax):
intarr = int2array(n)
intsum = sum(powArray(intarr, npow))
if intsum == n:
print intsum
totalsum += intsum
n += 1
from eulermath import int2array
if __name__ == "__main__":
# ndigmax = 3 # Test case, should give the 12th term, 144
ndigmax = 1000
ndigs = 1
a = 1
b = 1
n = 2 # Current term number
while ndigs < ndigmax:
nb = b + a
a = b
b = nb
n += 1
ndigs = len(int2array(b))
# print n, b
print "The first term to have over", ndigmax,
"digits is the", n, "th term = ", b
# Find the maximum digit sum of a^b, where a,b <= 100
from eulermath import int2array
if __name__ == "__main__":
nmax = 100
smax = 0
for a in range(1, nmax+1):
for b in range(1, nmax+1):
p = a**b
s = sum(int2array(p))
# print "%d^%d = %d, digit sum = %d" % (a,b,p,s)
if s > smax:
smax = s
# print "found a larger sum"
print "%d/%d complete" % (a, nmax)
print "The maximum digit sum is: %d" % (smax)
# Find the sum of the digits in the numerator
# for the 100th convergent of the continued
# fraction for e
from fractions import Fraction
from eulermath import int2array, frac2str, makecontfrac
def convterms_e(n):
enot = [0]*n
for x in range(n):
if x == 0:
enot[x] = 2
elif (x+2) % 3 == 1:
enot[x] = 2*((x+2)/3)
else:
enot[x] = 1
return enot
if __name__ == "__main__":
print convterms_e(10)
print makecontfrac(convterms_e(10))
t100 = makecontfrac(convterms_e(100))
snd = sum(int2array(t100.numerator))
print ("The sum of the digits in the numerator of the " +
"100th convergent of e is: %d" % (snd))
