30 is carréphylic - approach of √30 ~ 5.4772255751
Subsequent approximations of √30 - the position of a fraction indicates whether it is over or under the root-value.
| Diophantine equation: | s2-30p2 = 1 | | | |
| d = distance to nearest square N2: | +5 | | | |
| Smallest non-trivial s: | (2*25+5)/5 | rational: 11 | actual: 11 | ⇒ F=22 |
| Smallest non-trivial p: | 2*5/5 | rational: 2 | actual: 2 | ⇒ primus foldage=2 |
| v-value qt-blocks: | 52-30*12: | -5 | | |
| Number of series: | 7 | | | |
Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
| s | 1 | 11 | 241 | 5291 | 116161 | 2550251 | 55989361 | ... |
| p | 0 | 2 | 44 | 966 | 21208 | 465610 | 10222212 | ... |
| In the numerator: | U(1,11)22 | = | 1/2*U(2,22)22 | - | half the secundus of 22. |
| In the denominator: | U(0,2)22 | = | 2*U(0,1)22 | - | the 2-fold primus of 22. |
| as well as ... |
| In the numerator: | U(0,60)22 | = | 60*U(0,1)22 | - | the 30*2-fold primus of 22. |
| In the denominator: | U(1,11)22 | = | 1/2*U(2,22)22 | - | half the secundus of 22. |
| and ... |
| In the numerator: | U(-5,5)22 | = | 5*U(-1,1)22 | - | the 5-fold quartus of 22. |
| In the denominator: | U(1,1)22 | = | | - | the tertius of 22. |
