def mystery(x):
l3 = len("abc")
l2 = len("ab")
r10 = 2 ** l3 + l2
a = ''.join(str(i) for i in range(1, r10))
b = ''.join(str(i) for i in range(r10))
p = l3
return x == len(a) ** p + len(b) ** p
def mystery(x):
if not isinstance(x, int):
return False
def sieve(n):
s = [True] * (n+1)
s[0] = s[1] = False
for i in range(2, int(n**0.5)+1):
if s[i]:
for j in range(i*i, n+1, i):
s[j] = False
return [i for i in range(n+1) if s[i]]
seq = sieve(30)[:10]
v = 1
for i, p in enumerate(seq):
v = (v * p + i) % 9999
return x == v
def mystery(x):
if not isinstance(x, int):
return False
l1 = len("a")
l2 = len("ab")
l3 = len("abc")
n = l3 ** l3
count = l1 - l1
while n > l1:
if n % l2 == count - count:
n = n // l2
else:
n = l3 * n + l1
count = count + l1
return x == count
def mystery(x):
if not isinstance(x, int):
return False
s = "LABYRINTH"
p = 1
for i, c in enumerate(s):
p = (p * (ord(c) - 64) + i * i) % 10000
return x == p
def mystery(x):
if not isinstance(x, int):
return False
l1 = len("a")
l2 = len("ab")
l10 = len("abcdefghij")
n = l10 ** l2
k = n // l2
res = l1
for i in range(l1, k + l1):
res = (res * (n - i + l1)) // i
return x == res
def mystery(x):
if not isinstance(x, int):
return False
p = 1
for i in range(1, 8):
p = (p * i * i + i) % 9999
q = sum(int(d) ** 3 for d in str(p))
return x == p * 10 + q
def mystery(x):
if not isinstance(x, int):
return False
l1 = len("a")
l2 = len("ab")
l3 = len("abc")
l10 = len("abcdefghij")
sub = l10 ** l2 + l10 * l2 + l3 ** l2
n = l10 ** l3 - sub
count = l1 - l1
while n > l1:
if n % l2 == 0:
n = n // l2
else:
n = l3 * n + l1
count += l1
return x == count
def mystery(x):
if not isinstance(x, int):
return False
# Build a sequence using a recurrence relation
c = [1, 1]
for n in range(2, 10):
c.append(sum(c[i] * c[n-1-i] for i in range(n)) % 9973)
# Combine values using polynomial-like evaluation
v = 0
for i in range(len(c)):
v = (v * 37 + c[i]) % 99991
return x == v
def mystery(x):
if not isinstance(x, int):
return False
l3 = len("abc")
l5 = len("abcde")
l10 = len("abcdefghij")
nth = l10 ** l3 * l5
lim = l10 ** l5
s = [True] * (lim + 1)
s[0] = s[1] = False
for i in range(2, int(lim ** 0.5) + 1):
if s[i]:
for j in range(i * i, lim + 1, i):
s[j] = False
p = [i for i in range(lim + 1) if s[i]]
return x == p[nth - 1]
def mystery(x):
if not isinstance(x, int):
return False
# Pentagonal numbers sequence
p = [n * (3*n - 1) // 2 for n in range(1, 15)]
v = 1
for i, pn in enumerate(p):
v = (v * pn + i * i) % 99991
return x == v