QT-blocks involve the other two fabfour series that are always part of the set of series of a fractional approach, the quartus and the tertius.
We've defined a fraction's value 'v' = (numerator)2-n*(denominator)2. With regard to this, qt-blocks come in three kinds:
The value of 'v' is the same for all qt-blocks in a particular series.
For carréphobic numbers, all fractions involved are indeed multiples of the tertius and quartus.
Carréphylic numbers on the other hand always have a single tertius or quartus in the denominator.
From the first qt-block ⇒ the first non trivial sp-block
The following formulas hold for both carréphylic and carréphobic numbers. For the former they are inconsequential because the diophantine equation s2-np2 = 1 can be solved. For the latter they allow the calculation of 's' and 'p' in cases where a direct search fails.
As far as this investigation is concerned, I used them to determine the sp-blocks of √61 (1766319049 / 226153980) and √109 (158070671986249 / 15140424455100), both of which were out of range of Ed's fractional approximations program.
Since √nq2 = Q√n, s/p is an approximation of Q√n, so for √n itself: