#!/usr/bin/perl -w
use strict;

my @string; # Can I avoid using this array for the task?

while(<DATA>){
		s/\s//g;

		if (/^>/)
    		{  push(@string,'');
		   next;
		}	
		 chomp;
		 # concatenate current line
		 # to the last array item
             $string[-1] .= $_;

}
print $_+1," : ", $string[$_],"\n" foreach (0..$#string);

__DATA__
> Seq 1 (two lines)
AAAAAAAAAAAAA
CCAAAAAAAAAAA
> Seq 2 (two lines)
AAAAAAAAAAAAA
AAAAAAAAAAAAA
> Seq 3 (one line)
TTTTTTTTTTTTAACTGAAGATTCGC

##</code><code>##

1 : AAAAAAAAAAAAACCAAAAAAAAAAA
2 : AAAAAAAAAAAAAAAAAAAAAAAAAA
3 : TTTTTTTTTTTTAACTGAAGATTCGC