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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.
 1 0 1 2 3 4 5 11 60 71 82 93 104 115 241 1320 1561 1802 2043 2284 2525 5291 28980 34271 39562 44853 50144 55435 116161 636240 752401 868562 984723 1100884 1217045 2550251 13968300 16518551 19068802 21619053 24169304 26719555 55989361 306666360 ... 0 1 1 1 1 1 1 2 11 13 15 17 19 21 44 241 285 329 373 417 461 966 5291 6257 7223 8189 9155 10121 21208 116161 137369 158577 179785 200993 222201 465610 2550251 3015861 3481471 3947081 4412691 4878301 10222212 55989361 ...

 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.