Would using thunderbolt-to-hdmi help? Late 2013 Macbook Pro 15.4" 2.6Ghz

I connect HDMI and not always do the full spectrum of resolutions appear within the list of choices?

System Preferences (app) -&gt; Displays (preference icon) -&gt; Display (tab) -&gt; Scaled (tab) 

What would cause this? 

Monitor is more of a TV I guess: Seiki 4K 39-inch. 

Even if 4k would perhaps cause a problem, 1080p, 1080i, and even 1440x900 failed to appear a good portion of the time.

Is this perhaps a hardware issue with the MBP's HDMI port?

Would it help if I used the thunderbolt-to-HDMI cable instead? Perhaps because of a faulty HDMI port maybe?
Option+click Scaled

You can toggle between Apple’s easy-to-understand “Larger Text”–“More Space” icons mode and the other mode listing specific resolutions. To toggle, hold down the Option key while clicking Scaled radio button.





Retina

As for that comment “Don’t used scaled.” on the Question, that is wrong advice. Scaled options are Retina-style by default, more commonly known as HiDPI. Note the checkbox Show low resolution modes in the second screen shot above. Checking that box and choosing a resolution listed with the notation (low resolution) means you are disabling the Retina feature and scaling up the image crudely (wasting pixels).