bash-pure, 188 bytes

Result

WA

Code [DL]

#!bin/sh
for i in `seq 1 50`;do read j;k=`echo "ibase=2; $j"|bc`;for x in `seq 0 22`;do if [ $[$[$x*$[$x-1]]/2] -eq $k ];then echo -n 1;break;elif [ $x -eq 22 ];then echo -n 0;fi;done;done

stdin

11000100
01001110
01010101
00110111
10100110
00111001
01101001
10011001
10010011
00000001
01010010
01011011
01000010
11101101
10111110
00001010
01010011
00101100
00001111
00101101
01010100
11000111
01001111
11011101
11100100
00011100
10101010
00011100
10011100
11101011
11010010
00100100
11100111
10001000
11111101
10000000
01011011
10101011
00000011
00000110
10110001
10010001
00010101
01111000
10011110
00001100
00000000
00110001
01110101
10101110

stdout

stderr

/bin/bash: warning: setlocale: LC_ALL: cannot change locale (en_US.UTF-8)
/code.bash: line 2: seq: command not found

strace