python3, 46 bytes

Result

WA

Code [DL]

i=''
while 1:i=(1+8*int(input(i),2))**.5%1 or1

stdin

00000001
00011100
00110110
00100001
00011000
10011001
01000001
10011100
00011001
00000011
00100100
00100100
00000100
01000010
00001010
10101001
11010100
00000000
01101001
00010101
01011011
00000110
11010101
01111100
01001110
01101010
10100001
01101100
10001000
10101011
11001001
11101101
00110111
00000000
00001111
11010010
00010111
11001111
11010110
00101101
10111110
00111000
01111111
11111101
10000001
01111000
11100111
10111101
11110010
11100100

stdout

stderr

  File "/volume/CODE", line 2
    while 1:i=(1+8*int(input(i),2))**.5%1 or1
                                            ^
SyntaxError: invalid syntax

strace