2 is carréphylic - approach of √2 ~ 1.4142135624

Subsequent approximations of √2 - the position of a fraction indicates whether it is over or under the root-value.
 1 0 1 3 4 7 17 24 41 99 140 239 577 816 1393 3363 4756 8119 19601 27720 47321 114243 161564 275807 665857 941664 1607521 3880899 5488420 9369319 22619537 31988856 54608393 131836323 186444716 ... 0 1 1 2 3 5 12 17 29 70 99 169 408 577 985 2378 3363 5741 13860 19601 33461 80782 114243 195025 470832 665857 1136689 2744210 3880899 6625109 15994428 22619537 38613965 93222358 131836323 ...

 Diophantine equation: s2-2p2 = 1 d = distance to nearest square N2: +1 Smallest non-trivial s: (2*1+1)/1 rational: 3 actual: 3 ⇒ F=6 Smallest non-trivial p: 2*1/1 rational: 2 actual: 2 ⇒ primus foldage=2 v-value qt-blocks: 12-2*12: -1 Number of series: 3

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
 s 1 3 17 99 577 3363 19601 114243 665857 3880899 ... p 0 2 12 70 408 2378 13860 80782 470832 2744210 ...

 In the numerator: U(1,3)6 = 1/2*U(2,6)6 - half the secundus of 6. In the denominator: U(0,2)6 = 2*U(0,1)6 - the 2-fold primus of 6. as well as ... In the numerator: U(0,4)6 = 4*U(0,1)6 - the 2*2-fold primus of 6. In the denominator: U(1,3)6 = 1/2*U(2,6)6 - half the secundus of 6. and ... In the numerator: U(-1,1)6 = - the quartus of 6. In the denominator: U(1,1)6 = - the tertius of 6.