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110 is carréphylic - approach of √110 ~ 10.4880884817

Subsequent approximations of √110 - the position of a fraction indicates whether it is over or under the root-value.
 1 0 1 2 3 4 5 6 7 8 9 10 21 220 241 262 283 304 325 346 367 388 409 430 881 9240 ... 0 1 1 1 1 1 1 1 1 1 1 1 2 21 23 25 27 29 31 33 35 37 39 41 84 881 ...

 Diophantine equation: s2-110p2 = 1 d = distance to nearest square N2: +10 Smallest non-trivial s: (2*100+10)/10 rational: 21 actual: 21 ⇒ F=42 Smallest non-trivial p: 2*10/10 rational: 2 actual: 2 ⇒ primus foldage=2 v-value qt-blocks: 102-110*12: -10 Number of series: 12

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
 s 1 21 881 ... p 0 2 84 ...

 In the numerator: U(1,21)42 = 1/2*U(2,42)42 - half the secundus of 42. In the denominator: U(0,2)42 = 2*U(0,1)42 - the 2-fold primus of 42. as well as ... In the numerator: U(0,220)42 = 220*U(0,1)42 - the 110*2-fold primus of 42. In the denominator: U(1,21)42 = 1/2*U(2,42)42 - half the secundus of 42. and ... In the numerator: U(-10,10)42 = 10*U(-1,1)42 - the 10-fold quartus of 42. In the denominator: U(1,1)42 = - the tertius of 42.