23 is carréphylic - approach of √23 ~ 4.7958315233

Subsequent approximations of √23 - the position of a fraction indicates whether it is over or under the root-value.
101234514192411513916318721123568191611515520667178228973101241127532674439495522426484532006937529343051748574154096515676712108636264960112707040153566411800624220655843233054442595504575215534101170579127125624609673075...
01111113452429343944491421912401151139116311871211123516813916411515552246673937529389769101284112799326882439681552480264960132020813754561430704148595215412001156835232109552426507525127125624...

Diophantine equation:s2-23p2 = 1
d = distance to nearest square N2:-2
Smallest non-trivial s:(2*25-2)/2rational: 24actual: 24⇒ F=48
Smallest non-trivial p:2*5/2rational: 5actual: 5⇒ primus foldage=5
v-value tq-blocks:52-23*12:+2
Number of series:9

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
s1241151552242649601127125624...
p052401151555248026507525...

In the numerator:U(1,24)48=1/2*U(2,48)48-half the secundus of 48.
In the denominator:U(0,5)48=5*U(0,1)48-the 5-fold primus of 48.
as well as ...
In the numerator:U(0,115)48=115*U(0,1)48-the 23*5-fold primus of 48.
In the denominator:U(1,24)48=1/2*U(2,48)48-half the secundus of 48.
and ...
In the numerator:U(5,5)48=5*U(1,1)48-the 5-fold tertius of 48.
In the denominator:U(-1,1)48=-the quartus of 48.


23567810111213141517181920212223242627282930
31323334353738394041424344454647485051525354555657
58596061626365666768697071727374757677787980828384
858687888990919293949596979899101102103104105106107108109110