def allPerm(num1, num2, num3):
num1L = int2list(num1)
num2L = int2list(num2)
num3L = int2list(num3)
num1L.sort()
num2L.sort()
num3L.sort()
allPerms = False
if(num1L == num2L and num1L == num3L):
allPerms = True
else:
allPerms = False
return allPerms
return [1, div]
else:
[newNum, newDen] = recSq(depth, divList)
thisDen = div*newDen + newNum
thisNum = newDen
# print(str(depth) + " a " + str(thisNum) + "/" + str(thisDen))
return [thisNum, thisDen]
divList = []
thisEven = 2
while len(divList) <= 100:
divList.append(1)
divList.append(thisEven)
divList.append(1)
thisEven += 2
divList = divList[0:99]
[n, d] = recSqEntry(0, divList)
print(n)
print(d)
numList = int2list(n)
thisSum = sum(numList)
print(n / d)
print(thisSum)
finalDen = den
return [finalNum, finalDen]
def recSq(iterations):
iterations -= 1
if iterations <= 0:
return [1, 2]
else:
[newNum, newDen] = recSq(iterations)
thisDen = 2 * newDen + newNum
thisNum = newDen
return [thisNum, thisDen]
sys.setrecursionlimit(10000)
n = 0
d = 0
count = 0
for i in range(1, 1001):
[n, d] = recSqEntry(i)
nList = int2list(n)
dList = int2list(d)
if len(nList) > len(dList):
count += 1
# print(str(i) + " " + str(n) + "/" + str(d) + " " + str(count))
print(count)
from black_box import ispalindrome
from black_box import int2list
from black_box import list2int
foundNum = 0
for num in range(1, 10000):
# print(num)
found = False
number = num
for iterations in range(0,50):
numList = []
numList = int2list(number)
numList.reverse()
numRev = list2int(numList)
number = number + numRev
if(ispalindrome(int2list(number))):
# print(num)
# print(iterations)
# print(number)
found = True
foundNum += 1
break
print(9999-foundNum)
print(num)
print(len(oneList))
print(len(otherList))
if num in oneList:
continue
elif num in otherList:
continue
found = False
thisList = [num]
numSum = num
while not found:
# print(thisList[-1])
numList = int2list(numSum)
numSum = sum([pow(i,2) for i in numList])
# print(numSum)
if numSum in oneList:
for n in thisList:
oneList.append(n)
found = True
elif numSum in otherList:
for n in thisList:
otherList.append(n)
found = True
if(n < endNum):
count += 1
else:
# print("Append")
thisList.append(numSum)
# A googol (10^100) is a massive number: one followed by one-hundred zeros; 100^100 is
# almost unimaginably large: one followed by two-hundred zeros. Despite their size, the
# sum of the digits in each number is only 1.
# Considering natural numbers of the form, a^b, where a, b < 100, what is the maximum
# digital sum?
from black_box import int2list
from black_box import list2int
from math import pow
#had to do my own power function because it keeps the integer in long format
#instead of scientific notation
def myPower(aa, bb):
myPowerValue = 1
for i in range(1, bb+1):
myPowerValue *= aa
return myPowerValue
maxSum = 0
for a in range(1, 100):
for b in range(1,100):
num = myPower(a,b)
numList = int2list(int(num))
numListSum = sum(numList)
if(numListSum > maxSum):
maxSum = numListSum
print(maxSum)