Shell – how to delete a header without deleting other rows in linux

sed '
    N                                                       #append next line
    s/$/))/                                                 #add `))` to end
    s/\(\S*\s*\)\(.*\)\n\1/printf "%016d\n" \$((10#\2+10#/  #check Nos, form line
    t                                                       #to end if Nos equal
    s/))$//                                                 #remove `))`
    D                                                       #delete 1st line
    ' file |
bash

Regarding 45000 digits number please note that maximum number which bash can handle is

/* Minimum and maximum values a `signed long int' can hold.  */
#  if __WORDSIZE == 64
#   define LONG_MAX 9223372036854775807L
#  else
#   define LONG_MAX 2147483647L
#  endif

[ 1 ] /usr/include/limits.h

Perl to the rescue!

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

my $group_size = 3;

my @first = split ' ', <>;

my @groups;
my $start_index = 0;
while ($start_index < @first) {
    my $step = 1;
    while ( $step < $group_size
            && $start_index + $step < @first
            && $first[$start_index] == $first[ $start_index + $step ]
          ) {
        ++$step;
    }
    push @groups, $step;
    print $first[$start_index], ' ';
    $start_index += $step;
}
print "\n";

my @numbers = split ' ', <>;

my $last;
for my $size (@groups) {
    my @group = splice @numbers, 0, $size;
    my $value = $group[-1] - $group[0];
    $value = $group[0] - $last if 1 == $size;
    $last = $group[-1];
    print $value, ' ';
}
print "\n";

You haven't specified what should happen if the very first group has just one member.