Rare numbers: Difference between revisions

===naively optimized===

A mess of code that can return the first 5 rare numbers in 5m5s on a i7-7700k.

<syntaxhighlight lang="python">

# rare.py

# by xing216

import time as t

from functools import cache

@cache

def isSquare(n: int) ->bool:

if n < 0:

return False

if n == 0:

return True

while n&3 == 0:

n=n>>2

if n&7 != 1:

return False

if n==1:

return True

c = n%10

if c in {3, 7}:

return False

if n % 7 in {3, 5, 6}:

return False

if n % 9 in {2,3,5,6,8}:

return False

if n % 13 in {2,5,6,7,8,11}:

return False

if c == 5:

if (n//10)%10 != 2:

return False

if (n//100)%10 not in {0,2,6}:

return False

if (n//100)%10 == 6:

if (n//1000)%10 not in {0,5}:

return False

else:

if (n//10)%4 != 0:

return False

s = (len(str(n))-1) // 2

x = (10**s) * 4

A = {x, n}

while x * x != n:

x = (x + (n // x)) >> 1

if x in A:

return False

A.add(x)

return True

@cache

def main() -> None:

r = 1

start = t.time()

while True:

strr = str(r)

if int(strr[0]) % 2 != 0:

r += int('1' + (len(strr)-1)*'0' )

r1 = int(strr[::-1])

x = r + r1

y = r - r1

if isSquare(x) and isSquare(y) and r != r1:

print(f'success: {r} ~{t.time()-start}s')

r+=1

if __name__ == '__main__':

main()

</syntaxhighlight>