streem, 94 bytes

Result

AC

Code [DL]

f={case 0->0
case x->f(int(x/10))*2+x%2}
stdin|{x->if(sqrt(f(number(x))*8+1)%1>0)0else 1}|puts

stdin

01000011
01111010
01100101
00111010
01000110
01110111
10001000
10011001
00011000
01001001
10011000
10100101
00111000
00101101
11001110
00000110
00000011
00001111
01011110
00110111
00100100
01011011
00110101
01111000
01111111
10100111
11100111
11010010
01000010
00001010
01101001
00101000
00000000
00101100
11111101
01001110
10010100
00001101
11101110
00010101
10111110
00011100
10101011
11100010
10011110
10011001
01000010
00000001
00110110
01111011

stdout

0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0

stderr

strace