def find_smallest_counter():
curr_comp = 9
while True:
primes = [i for i in prime_gen(max_val=curr_comp + 1)]
if curr_comp not in primes and not any(
is_square((curr_comp - p) / 2) for p in primes):
return curr_comp
curr_comp += 2
def find_smallest_counter():
curr_comp = 9
while True:
primes = [i for i in prime_gen(max_val=curr_comp + 1)]
if curr_comp not in primes and not any(is_square((curr_comp - p)/2)
for p in primes):
return curr_comp
curr_comp += 2
def is_triangular(tn):
'''Leverages:
The inverse of triangular: n = -1/2 + 1/2 * sqrt(1 + 8 * tn)
Therefore, 1 + 8 * pn must be square for tn to be triangular.
Also, since n must be an integer, the evaluated sqrt must be odd
'''
special_factor = 1 + 8 * tn
if is_square(special_factor):
given_root = int(sqrt(special_factor))
if given_root % 2 == 1:
return True
return False
def is_triangular(tn):
'''Leverages:
The inverse of triangular: n = -1/2 + 1/2 * sqrt(1 + 8 * tn)
Therefore, 1 + 8 * pn must be square for tn to be triangular.
Also, since n must be an integer, the evaluated sqrt must be odd
'''
special_factor = 1 + 8 * tn
if is_square(special_factor):
given_root = int(sqrt(special_factor))
if given_root % 2 == 1:
return True
return False
def is_hexagonal(hn):
'''Leverages:
The inverse of hexagonal: n = -1/4 + 1/4 * sqrt(1 + 8 * hn)
Therefore, 1 + 8 * hn must be square for hn to be hexagonal.
Also, since n must be an integer, the evaluated sqrt must:
Have a modulus of 3 with 4
'''
special_factor = 1 + 8 * hn
if is_square(special_factor):
given_root = int(sqrt(special_factor))
if given_root % 4 == 3:
return True
return False
def is_hexagonal(hn):
'''Leverages:
The inverse of hexagonal: n = -1/4 + 1/4 * sqrt(1 + 8 * hn)
Therefore, 1 + 8 * hn must be square for hn to be hexagonal.
Also, since n must be an integer, the evaluated sqrt must:
Have a modulus of 3 with 4
'''
special_factor = 1 + 8 * hn
if is_square(special_factor):
given_root = int(sqrt(special_factor))
if given_root % 4 == 3:
return True
return False
def is_pentagonal(pn):
'''Leverages:
The inverse of pentagonal: n = 1/6 + 1/6 * sqrt(1 + 24 * pn)
Therefore, 1 + 24 * pn must be square for pn to be pentagonal.
Also, since n must be an integer, the evaluated sqrt must:
Have a modulus of 5 with 6
'''
special_factor = 1 + 24 * pn
if is_square(special_factor):
given_root = int(sqrt(special_factor))
if given_root % 6 == 5:
return True
return False