Firstly, you should calculate again. You have the wrong calculation for the sub-pixels per inch and what you called "True PPI" of Pentile screen.

Secondly, you don't understand anything about Pentile technology. It takes the advantage of strong luminance green pixels of OLED to reduce the number of total sub-pixels without making a big depression on sharpness. If you say the sharpness depends on the number of sub-pixels only, so this technology is useless? Besides, it also depends on the stripe layout. On S4, it's diamond shape, which is way better than the implementation on S3

The redundant space is minimal and to be the same, not different big-small gaps flike on S3 (which is one of the main culprit of Jagginess on S3)
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Edit: To be clear here, here are the calculation for subpixels per inch.
1920 x 1080 at 4.7"(HTC One), 3 subpixels per pixel -> 6,220,800 subpixels = 3,325.5 x 1,870.6 subpixels (16:9)
811 subpixels per inch
1920 x 1080 at 5" (Samsung Galaxy S4), 2 subpixels per pixel -> 4,147,200 subpixels = 2,715.3 x 1,527.3 subpixels (16:9)
623 subpixels per inch

In addition, the subpixels per inch of iPhone 5 (329ppi) is 565 and of Z10 (347 ppi) is 615.
And here is the comparison of sharpness, S4 (what you said has the "True PPI" of 294) looks way sharper than iPhone 5 (with the so-called Retina display) under the microscope