c *= 2
if c > a:
break
if a-c in primeList:
return True
return False
# ********************************************************************
from utils import prime, sortedList
import time
startTime = time.time()
primeList = sortedList([])
primeList.add(2)
squareList = sortedList([])
squareList.addList([1,4])
start = 1 # en fait, 3
n = start
bool = True
while bool:
n += 2
squareList.add(n**2)
squareList.add((n+1)**2)
if prime(n):
# 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
# It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 - 22 = 48,
# is not pentagonal.
# Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference are
# pentagonal and D = |Pk - Pj| is minimised; what is the value of D?
from utils import sortedList
import time
startTime = time.time()
pentagonal = lambda n : n*(3*n - 1)//2
pentagonalList = sortedList([])
size = 2750
for n in range(1, size):
pentagonalList.add(pentagonal(n))
D = pentagonalList[-1] - pentagonalList[0]
for j in range(len(pentagonalList)):
if not j % (size//100):
print('.', end="", flush=True)
for k in range(j, len(pentagonalList)):
pj = pentagonalList[j]
pk = pentagonalList[k]
if len(list) != 9: return False for i in range(len(list)): if list[i] != i+1: return False return True # retourne une liste contenant tout les chiffres de a, b et a*b def mk(a,b): result = cut(a) result.extend(cut(b)) result.extend(cut(a*b)) result.sort() return result # ****************************************************************************** result = sortedList([]) for i in range(1,1000): for j in range(1,10000): if i*j >= 10000: break; if pandigital(mk(i,j)): result.add(i*j) print(result.sum())
# 3^2=9, 3^3=27, 3^4=81, 3^5=243
# 4^2=16, 4^3=64, 4^4=256, 4^5=1024
# 5^2=25, 5^3=125, 5^4=625, 5^5=3125
# If they are then placed in numerical order, with any repeats removed, we
# get the following
# sequence of 15 distinct terms:
# 4, 10, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
# How many distinct terms are in the sequence generated by a^b for
# 2 <= a < 100 and 2 <= b <= 100?
from utils import sortedList
list = sortedList([])
for a in range(2,101):
for b in range(2,101):
list.add(a**b)
print(list.size())