def test3(limit):
matches = [16]
test = 15
interval = 1
direction = 1
ratio = 3
while matches[-1] < limit:
if test % 2 == 0:
h1 = heron_area_squared(test, test + 1, test + 1)
if is_perfect_square(h1):
perimeter = test + test + 1 + test + 1
ratio = perimeter / matches[-1]
matches.append(perimeter)
test = int(test * ratio)
interval = 1
continue
else:
h2 = heron_area_squared(test, test, test + 1)
if is_perfect_square(h2):
perimeter = test + test + test + 1
# ratio = perimeter / matches[-1]
matches.append(perimeter)
test = int(test * ratio)
interval = 1
continue
test += interval * direction
interval += 1
direction *= -1
return sum(matches[:-1])
def test(limit):
a = 1
while a < limit:
if a % 2 == 0:
h1 = heron_area_squared(a, a + 1, a + 1)
if is_perfect_square(h1):
print(a, a + 1, a + 1, h1, (3 * a + 2) / 2)
else:
h2 = heron_area_squared(a, a, a + 1)
if is_perfect_square(h2):
print(a, a, a + 1, h2, (3 * a + 1) / 2)
a += 1
def frac_decompose(n, p=None):
if is_perfect_square(n): return 0
array = [int_sqrt(n)]
p = p or int_sqrt(n) * 2 + 5
s = square_root(n, p)
br = int_sqrt(n) * 2 + 5
while True:
inc = 1
i = 1
while True:
if i > br:
return frac_decompose(n, p * 2)
array.append(i + inc)
x = long_div(*frac(array), p)
array.pop()
array.append(i)
y = long_div(*frac(array), p)
if (s > x) ^ (s > y):
if inc > 1:
inc = 1
array.pop()
continue
else:
break
array.pop()
i += inc
if i == 4 and inc == 1:
inc = 10
if array[-1] == array[0] * 2:
print(array)
return len(array) - 1
def test4(limit):
matches = [16]
side1 = 6
direction = 1
ratio = 2 + sqrt(3)
while matches[-1] < limit:
side2 = side1 if side1 % 2 == 1 else side1 + 1
area_squared = heron_area_squared(side1, side2, side1 + 1)
print(area_squared)
if is_perfect_square(area_squared):
perimeter = side1 + side2 + side1 + 1
matches.append(perimeter)
side1 = int(side1 * ratio)
direction *= -1
continue
side1 += direction
return sum(matches[:-1])
def is_possibly_odd_period(n, evens):
if is_perfect_square(n - 1): return True
prime_factors = set()
divisor = 3
while not n % 2:
if 2 in prime_factors: return False
prime_factors.add(2)
n //= 2
while divisor * divisor <= n:
if not n % divisor:
if divisor in evens: return False
prime_factors.add(divisor)
n //= divisor
else:
divisor += 2
if n in evens: return False
return True
from math import sqrt, factorial
from itertools import combinations
from simplemath import is_perfect_square, int_sqrt
c = lambda n, r: factorial(n) // (factorial(r) * factorial(n - r))
is_triple = lambda a, b: is_perfect_square(a**2 + b**2)
def euclid(m, n):
a = m**2 - n**2
b = 2 * m * n
c = m**2 + n**2
return (a, b, c)
def euclid_gen(max_legs):
limit = int_sqrt(max_legs // 2) + 1
for i in range(1, limit):
for j in range(i + 1, limit):
yield euclid(j, i)
def run(m):
total = 0
for triple in euclid_gen(3 * m):
total += score(sorted(triple), m)
return total
# 4x^2 > 3*lim
# x^2 == 1.5*lim