bash-pure, 182 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 1;break;elif [ $x -eq 22 ];then echo 0;fi;done;done

stdin

00001010
11001101
00101111
00000000
11111001
01100100
00101101
00011100
10000111
00000111
10010110
01001110
11110100
01111000
00000100
01101001
00010011
10011001
11010010
11010101
10110101
00010101
10101011
11100111
00000110
00001111
01010111
10001110
01110110
00000011
01011011
11111100
00011100
01010001
10101111
01110000
00100100
10010111
01000010
11110111
00000001
01111101
10111110
00010100
00110111
00100100
00110010
11111101
01111100
10001000

stdout

stderr

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

strace