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95 is carréphylic - approach of √95 ~ 9.7467943448

Subsequent approximations of √95 - 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 19 29 39 380 419 458 497 536 575 614 653 692 731 770 1501 2271 3041 29640 ... 0 1 1 1 1 1 1 1 1 1 1 1 2 3 4 39 43 47 51 55 59 63 67 71 75 79 154 233 312 3041 ...

 Diophantine equation: s2-95p2 = 1 d = distance to nearest square N2: -5 Smallest non-trivial s: (2*100-5)/5 rational: 39 actual: 39 ⇒ F=78 Smallest non-trivial p: 2*10/5 rational: 4 actual: 4 ⇒ primus foldage=4 v-value t/q-fraction: 102-95*12: +5 v-value q/t-fraction: 192-95*22: -19 Number of series: 14

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
 s 1 39 3041 ... p 0 4 312 ...

 In the numerator: U(1,39)78 = 1/2*U(2,78)78 - half the secundus of 78. In the denominator: U(0,4)78 = 4*U(0,1)78 - the 4-fold primus of 78. as well as ... In the numerator: U(0,380)78 = 380*U(0,1)78 - the 95*4-fold primus of 78. In the denominator: U(1,39)78 = 1/2*U(2,78)78 - half the secundus of 78. and ... In the numerator: U(10,10)78 = 10*U(1,1)78 - the 10-fold tertius of 78. In the denominator: U(-1,1)78 = - the quartus of 78. and ... In the numerator: U(-19,19)78 = 19*U(-1,1)78 - the 19-fold quartus of 78. In the denominator: U(2,2)78 = 2*U(1,1)78 - the 2-fold tertius of 78.