https://projecteuler.net/problem=49
+The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
+There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
+What 12-digit number do you form by concatenating the three terms in this sequence?
+def sieve_of_eratosthenes(number):
+ primes = []
+ prospects = [n for n in range(2, number)]
+ while prospects:
+ p = prospects[0]
+ prospects = [x for x in prospects if x % p != 0]
+ primes.append(p)
+ if p * p > number:
+ break
+ return primes + prospects
+
+ps = [p for p in sieve_of_eratosthenes(10000) if p > 1000]
+d = {}
+for p in ps:
+ s = "".join(sorted(str(p)))
+ try:
+ d[s].append(p)
+ except KeyError:
+ d[s] = [p]
+
+pss = [value for key, value in d.items() if len(value) >= 3]
+def find_increasing_sequence(xs):
+ deltas = [(xs[j] - xs[i], i, j)
+ for i in range(0, len(xs) - 1)
+ for j in range(i + 1, len(xs))
+ ]
+ d = {}
+ for delta, i, j in deltas:
+ if delta in d and d[delta][-1] == i:
+ d[delta].append(j)
+ else:
+ d[delta] = [i, j]
+ for delta, sequence in d.items():
+ if len(sequence) == 3:
+ return [xs[index] for index in sequence]
+ return []
+
+s = [find_increasing_sequence(ps) for ps in pss if find_increasing_sequence(ps)]
+print(s)
+s = int("".join(map(str, s[1])))
+assert(s == 296962999629)
+print(s)
+Congratulations, the answer you gave to problem 49 is correct.
+You are the 49654th person to have solved this problem.
+Nice work, failx, you've just advanced to Level 2 . +46903 members (5.43%) have made it this far.
+This problem had a difficulty rating of 5%. The highest difficulty rating you have solved remains at 5%.
+
+