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80 is carréphylic - approach of √80=4√5 ~ 8.9442719100

Subsequent approximations of √80 - 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 80 89 98 107 116 125 134 143 152 161 1440 1601 1762 1923 2084 2245 2406 2567 2728 2889 25840 28729 31618 34507 37396 40285 43174 46063 48952 51841 463680 515521 567362 619203 671044 722885 774726 826567 878408 930249 8320400 9250649 10180898 11111147 12041396 12971645 13901894 14832143 15762392 16692641 149303520 165996161 182688802 199381443 216074084 232766725 249459366 266152007 282844648 299537289 2679142960 ... 0 1 1 1 1 1 1 1 1 1 1 9 10 11 12 13 14 15 16 17 18 161 179 197 215 233 251 269 287 305 323 2889 3212 3535 3858 4181 4504 4827 5150 5473 5796 51841 57637 63433 69229 75025 80821 86617 92413 98209 104005 930249 1034254 1138259 1242264 1346269 1450274 1554279 1658284 1762289 1866294 16692641 18558935 20425229 22291523 24157817 26024111 27890405 29756699 31622993 33489287 299537289 ...

80 is one less than a square, so the exception mentioned in on root approach applies: 161 and 18, as rendered by the formula, are not the first non-trivial sp-block, but the second, the first being 9 and 1 because 92-80*12 = 1 satisfies the diophantine equation.
 Diophantine equation: s2-80p2 = 1 d = distance to nearest square N2: -1 Smallest non-trivial s: (2*81-1)/1 rational: 161 actual: 161 (9) ⇒ F=322 (18) Smallest non-trivial p: 2*8/1 rational: 18 actual: 18 (1) ⇒ primus foldage=18 (1) v-value tq-blocks: 82-80*12: -16 Number of series: 10

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
 s 1 9 161 2889 ... p 0 1 18 323 ...

 In the numerator: U(1,9)18 = 1/2*U(2,18)18 - half the secundus of 18. In the denominator: U(0,1)18 = - the primus of 18. as well as ... In the numerator: U(0,80)18 = 80*U(0,1)18 - the 80-fold primus of 18. In the denominator: U(1,9)18 = 1/2*U(2,18)18 - half the secundus of 18. and ... In the numerator: U(-8,8)18 = 8*U(-1,1)18 - the 8-fold quartus of 18. In the denominator: U(1,1)18 = - the tertius of 18.