Here's a quick example showing your problem can be done using a binary search, even though the "25" is not in the list.

Note: my version returns only elements actually in the list. If you want all the integers in between, just return $F[$lo_pos]..$F[$hi_pos].

Update: It now appears that the index positions are wanted instead. No problem, that's just $lo_pos..$hi_pos.

use strict;
use Search::Binary;

my $lastIndex;

sub reader {
  my ($handle, $val, $index) = @_;
  if (!defined $index) {
     $lastIndex++;
  } else {
     $lastIndex = $index;
  }
  return ($val <=> $handle->[$lastIndex], $lastIndex);
}

my @F = (
      1,
      2,
      4,
      8,
      16,
      32..64
     );

sub range{
  my($lo, $hi) = @_;
  my $lo_pos = binary_search(0,$#F,$lo,\&reader,\@F);
  my $hi_pos = binary_search(0,$#F,$hi,\&reader,\@F);
  $hi_pos = $#F if ($hi_pos > $#F);
  return @F[$lo_pos..$hi_pos];
}

print join(',', range(25,35)), "\n";
print join(',', range(50,75)), "\n";
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