61 is carréphobic - approach of √61 ~ 7.8102496759

Here Ed's program failed to provide the last 3 fractions before the sp-block. The sp-block itself was derived from the qt-block, after it was identified as such. The positioning of the missing fractions is derived from a property of roots with the qt-block in the middle of the section: corresponding fractions in the first and second half are on opposite sides of the root-value.
Subsequent approximations of √61.
101234567823313986125164289453107015234116563918440240792971826182329154132125935097738069541041344013146984913798291849678231952751089037428430974795717176387269243446359664590520989244638623???176631904913795392780...
01111111113451116213758137195527722236130833805335233732841133449384874352548563536015817666923682729698565412895111312480982199211344730981427161159002531322766???2261539801766319049...

Diophantine equation:s2-61p2 = 1
d = distance to nearest square N2:-3
Smallest non-trivial s:(2*64-3)/3rational: 125/3actual: 1766319049⇒ F=3532638098
Smallest non-trivial p:2*8/3rational: 16/3actual: 226153980⇒ primus foldage=226153980
v-value qt-blocks:297182-61*38052:-1
Number of series:47

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
s11766319049...
p0226153980...

In the numerator:U(1,1766319049)3532638098=1/2*U(2,3532638098)3532638098-half the secundus of 3532638098.
In the denominator:U(0,226153980)3532638098=226153980*U(0,1)3532638098-the 226153980-fold primus of 3532638098.
as well as ...
In the numerator:U(0,13795392780)3532638098=13795392780*U(0,1)3532638098-the 61*226153980-fold primus of 3532638098.
In the denominator:U(1,1766319049)3532638098=1/2*U(2,3532638098)3532638098-half the secundus of 3532638098.
and ...
In the numerator:U(-29718,29718)3532638098=29718*U(-1,1)3532638098-the 29718-fold quartus of 3532638098.
In the denominator:U(3805,3805)3532638098=3805*U(1,1)3532638098-the 3805-fold tertius of 3532638098.


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58596061626365666768697071727374757677787980828384
858687888990919293949596979899101102103104105106107108109110