#!/usr/bin/perl
use strict;
use warnings;

# 847021

=head OUTPUT OF THIS VERS:

>Long_DNA_Scaffold.0
atgctagsctgtagctagctagtcgatgctagtagct
ttagctagctgatgctagtcgatgctagtcatctagc

>Long_DNA_Scaffold.1

tagctagctagctgatcgtagctagtcgtagctagct
ggtcgatgctgatcgtagctgatgctagtcgatgcta
>                                       # removal of ">" and blank lines left as an exercise....
>Long_DNA_Scaffold2.0
atgctagsctgtagctagctagtcgatgctagtagct
tagctagctgatcgtagctagctgatgctagctagtc

>Long_DNA_Scaffold2.1

tagctagctagctgatgctagctagtcgatcgtagct
ggctagtgctagtgctagctgatgctagtcgtagctg

=cut

my $file = "847021.txt";
open (IN, '<', $file) or die "Can't open $file: $!";    # test your file opens!

$/=">";
my $i=0;
my $separator_count=0;
my (@seq, $seq, @name, $name);

while (<IN>) {
	if(/^(\S+)?.*?\n(.*)/ms) {
		# $i++;                                         # this creates an empty ("undef") element 0 in the arrays; mis-located; moved
		$seq[$i]=$2; 
		$name[$i]=$1; 
	} else {
		$separator_count++;
		if ($separator_count > 1) {
			print "No match for current data: $_\n\n"; 	 # one instance is expected because the data begins with record separator; don't show it
		} else {
			next;                                        # create no undef $arr[0]
		}
  	}
$i++;                                                    # re-located from line 57
}
close IN;
print "\n";

for my $j(0..$#seq) {                                    #   $#seq: index of last element. 0..$i replacing OP's 1..$i

	$name[$j] =~ tr/>//;                                 # replaces OP's mis-coded tr//; see toolic's reply, above re tr syntax
	$seq[$j] =~ tr/>//;
	my @sequence=split(/N+/,$seq[$j]);

	my $n=length(@sequence);
	my$seqs_to_print=$n;                                 # OP's decrement caused failure to print second elements of @seq
	for my $k(0..$seqs_to_print){                        # use $i, $j, $k for counters; $x and company are typically for substantive data  
	print ">$name[$j].$k\n";
	print "$sequence[$k]\n";
	}
	$j++;
}