13 is carréphobic - approach of √13 ~ 3.6055512755
Subsequent approximations of √13 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-13p2 = 1 | | | |
| d = distance to nearest square N2: | -3 | | | |
| Smallest non-trivial s: | (2*16-3)/3 | rational: 29/3 | actual: 649 | ⇒ F=1298 |
| Smallest non-trivial p: | 2*4/3 | rational: 8/3 | actual: 180 | ⇒ primus foldage=180 |
| v-value qt-blocks: | 182-13*52: | -1 | | |
| Number of series: | 15 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 649 | 842401 | 1093435849 | ... |
| p | 0 | 180 | 233640 | 303264540 | ... |
| In the numerator: | U(1,649)1298 | = | 1/2*U(2,1298)1298 | - | half the secundus of 1298. |
| In the denominator: | U(0,180)1298 | = | 180*U(0,1)1298 | - | the 180-fold primus of 1298. |
| as well as ... |
| In the numerator: | U(0,2340)1298 | = | 2340*U(0,1)1298 | - | the 13*180-fold primus of 1298. |
| In the denominator: | U(1,649)1298 | = | 1/2*U(2,1298)1298 | - | half the secundus of 1298. |
| and ... |
| In the numerator: | U(-18,18)1298 | = | 18*U(-1,1)1298 | - | the 18-fold quartus of 1298. |
| In the denominator: | U(5,5)1298 | = | 5*U(1,1)1298 | - | the 5-fold tertius of 1298. |
