18 is carréphylic - approach of √18=3√2 ~ 4.2426406871

Subsequent approximations of √18 - the position of a fraction indicates whether it is over or under the root-value.
 1 0 1 2 3 4 13 17 72 89 106 123 140 437 577 2448 3025 3602 4179 4756 14845 19601 83160 102761 122362 141963 161564 504293 665857 2824992 3490849 4156706 4822563 5488420 17131117 22619537 95966568 ... 0 1 1 1 1 1 3 4 17 21 25 29 33 103 136 577 713 849 985 1121 3499 4620 19601 24221 28841 33461 38081 118863 156944 665857 822801 979745 1136689 1293633 4037843 5331476 22619537 ...

 Diophantine equation: s2-18p2 = 1 d = distance to nearest square N2: +2 Smallest non-trivial s: (2*16+2)/2 rational: 17 actual: 17 ⇒ F=34 Smallest non-trivial p: 2*4/2 rational: 4 actual: 4 ⇒ primus foldage=4 v-value qt-blocks: 42-18*12: -2 Number of series: 7

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
 s 1 17 577 19601 665857 22619537 ... p 0 4 136 4620 156944 5331476 ...

 In the numerator: U(1,17)34 = 1/2*U(2,34)34 - half the secundus of 34. In the denominator: U(0,4)34 = 4*U(0,1)34 - the 4-fold primus of 34. as well as ... In the numerator: U(0,72)34 = 72*U(0,1)34 - the 18*4-fold primus of 34. In the denominator: U(1,17)34 = 1/2*U(2,34)34 - half the secundus of 34. and ... In the numerator: U(-4,4)34 = 4*U(-1,1)34 - the 4-fold quartus of 34. In the denominator: U(1,1)34 = - the tertius of 34.