One line in awk :

cat [your file]  | awk 'BEGIN{COUNTER=1}{print ">seq_"COUNTER"\n"$1; COUNTER++;}' > output.fa

Another way to do this is:

$ perl below-script.pl sequence-input.txt

#!/usr/bin/perl                                                             

open (INPUT, $ARGV[0]) or die $!;                                           
open (OUTPUT, ">Output.fa");                                                

while (<INPUT>){                                                            
    chomp;                                                                  
    ($seq) = split("\t");                                                   
    print ">seq_$.\n$seq\n";                                                
}                                                                           

close (OUTPUT);                                                             
close (INPUT);

try this:

#!/usr/bin/perl -w
print"Enter Input File: ";   
$in=<STDIN>;
chomp $in;
open FH, "<$in";
open OUT, ">output_sequence.fasta";
$count=0;
@in=<FH>;  
@line=split/\n/,"@in";   

foreach (@line)    
{    
@word=split('\t',$_);  
$count++;
$word[0]=~s/ +//;              
print OUT ">seq_$count\n$word[0]\n"; 
}
close FH;
close OUT;

Here's another option: perl -lane 'print "seq_$.\n$F[0]"' inFile >outFile

Or as a script:

use strict;
use warnings;

    while (<>) {
        print "seq_$.\n" . (/(\S+)/)[0] . "\n";
    }

Usage: perl script.pl inFile >outFile

Output of both on your dataset:

seq_1
GGCGGATGTAGCCACGTGGATC
seq_2
AGCTGCTGTAGGGTATGGCGAGCC
seq_3
TGGATAATGGACGAGTACCGCCTG

Hope this helps!