[ Link to other thread for reference: printing the length of string variables ]

The following uses a single-line lookahead, and it happens to only keep one sequence in memory at a time.

use strict;
use warnings;

my $fh = \*DATA;

my $line = <$fh>;
while (defined($line)) {
   my $head = $line;

   $line = <$fh>;
   die("Premature EOF\n") if !defined($line);
   chomp( my $seq = $line );

   for (;;) {
      $line = <$fh>;
      last if !defined($line) || $line =~ /^>/;
      chomp( $seq .= $line );
   }

   my $len = length($seq);
   $head =~ s/(length=)\d+/$1$len/;
   print("$head$seq\n");
}

__DATA__
>IDnumber1 length=350
AGCTG
AAGTCGCT
>IDnumber2 length=350
AGAACGT
ACC
>IDnumber3 length=350
AGC
ACTTCGCTAACT
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