71 is carréphobic - approach of √71 ~ 8.4261497732

Subsequent approximations of √71 - 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 17 42 59 278 337 396 455 514 969 1483 1997 3480 29323 32803 36283 39763 43243 46723 50203 53683 57163 117806 292775 410581 1935099 2345680 2756261 3166842 3577423 6744265 10321688 13899111 24220799 204088080 ... 0 1 1 1 1 1 1 1 1 1 2 5 7 33 40 47 54 61 115 176 237 413 3480 3893 4306 4719 5132 5545 5958 6371 6784 13981 34746 48727 229654 278381 327108 375835 424562 800397 1224959 1649521 2874480 24220799 ...

 Diophantine equation: s2-71p2 = 1 d = distance to nearest square N2: +7 Smallest non-trivial s: (2*64+7)/7 rational: 135/7 actual: 3480 ⇒ F=6960 Smallest non-trivial p: 2*8/7 rational: 16/7 actual: 413 ⇒ primus foldage=413 v-value tq-blocks: 592-71*72: +2 Number of series: 21

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
 s 1 3480 24220799 ... p 0 413 2874480 ...

 In the numerator: U(1,3480)6960 = 1/2*U(2,6960)6960 - half the secundus of 6960. In the denominator: U(0,413)6960 = 413*U(0,1)6960 - the 413-fold primus of 6960. as well as ... In the numerator: U(0,29323)6960 = 29323*U(0,1)6960 - the 71*413-fold primus of 6960. In the denominator: U(1,3480)6960 = 1/2*U(2,6960)6960 - half the secundus of 6960. and ... In the numerator: U(59,59)6960 = 59*U(1,1)6960 - the 59-fold tertius of 6960. In the denominator: U(-7,7)6960 = 7*U(-1,1)6960 - the 7-fold quartus of 6960.