Loop com string.

unit Unit1;

interface

uses
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls;

type
  TForm1 = class(TForm)
    txt_inicio: TEdit;
    txt_fim: TEdit;
    Memo1: TMemo;
    Button1: TButton;
    procedure Button1Click(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

implementation

{$R *.dfm}

procedure TForm1.Button1Click(Sender: TObject);
var
i: integer;
begin
for I := strtoint(txt_inicio.Text;) to strtoint(txt_fim.Text;) - 1 do
begin
  memo1.Lines.Add(inttostr(i));
end;
end;

end.