Reclaim hard drive space from deleted partition and reclaim Apple bootloader

The disk giving you problems uses the GUID partition table (GPT) to define the its layout. You provided me with the relevant contents of this table when you posted the output from the command sudo gpt -r show /dev/disk0. These values appear to be correct, except for the entry with an index of 3. This entry is shown below.

      480002496    1269536      3  GPT part - 48465300-0000-11AA-AA11-00306543ECAC

The start and size values of 480002496 and 1269536, respectively, are OK, but the contents should be GPT part - 426F6F74-0000-11AA-AA11-00306543ECAC.

To correct the problem you need to boot to OS X Internet Recovery and enter the following commands in a Terminal window.

gpt  -r  show  /dev/disk0
diskutil  unmountDisk  /dev/disk0
gpt  remove  -i  3  /dev/disk0
diskutil  unmountDisk  /dev/disk0
gpt  add  -i  3  -b  480002496  -s  1269536  -t  426F6F74-0000-11AA-AA11-00306543ECAC  /dev/disk0

Once completed, you can boot back to OS X and open the Disk Utility application. The "Recovery HD" partition should no longer appear. You will need to move the slider on the "Macintosh HD" partition as far down as it will go. Click the "Apply" button to recover the free space.

Note: The "Recovery HD" partition has not been deleted. Normally, it is hidden by the Disk Utility application. The partition will still appear when using the diskutil list command. When you move the slider down be aware the Disk Utility application will have to relocate the "Recovery HD" partition to the end of the disk. This can take a while, so be patient after clicking the "Apply" button.