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24 is carréphylic - approach of √24=2√6 ~ 4.8989794856

Subsequent approximations of √24 - the position of a fraction indicates whether it is over or under the root-value.
 1 0 1 2 3 4 5 24 29 34 39 44 49 240 289 338 387 436 485 2376 2861 3346 3831 4316 4801 23520 28321 33122 37923 42724 47525 232824 280349 327874 375399 422924 470449 2304720 2775169 3245618 3716067 4186516 4656965 22814376 27471341 32128306 36785271 41442236 46099201 225839040 ... 0 1 1 1 1 1 1 5 6 7 8 9 10 49 59 69 79 89 99 485 584 683 782 881 980 4801 5781 6761 7741 8721 9701 47525 57226 66927 76628 86329 96030 470449 566479 662509 758539 854569 950599 4656965 5607564 6558163 7508762 8459361 9409960 46099201 ...

24 is one less than a square, so the exception mentioned in on root approach applies: 49 and 10, as rendered by the formula, are not the first non-trivial sp-block, but the second, the first being 5 and 1 because 52-24*12 = 1 satisfies the diophantine equation.
 Diophantine equation: s2-24p2 = 1 d = distance to nearest square N2: -1 Smallest non-trivial s: (2*25-1)/1 rational: 49 actual: 49 (5) ⇒ F=98 (10) Smallest non-trivial p: 2*5/1 rational: 10 actual: 10 (1) ⇒ primus foldage=10 (1) v-value qt-blocks: 42-24*12: -8 Number of series: 6

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
 s 1 5 49 485 4801 47525 470449 4656965 46099201 ... p 0 1 10 99 980 9701 96030 950599 9409960 ...

 In the numerator: U(1,5)10 = 1/2*U(2,10)10 - half the secundus of 10. In the denominator: U(0,1)10 = - the primus of 10. as well as ... In the numerator: U(0,24)10 = 24*U(0,1)10 - the 24-fold primus of 10. In the denominator: U(1,5)10 = 1/2*U(2,10)10 - half the secundus of 10. and ... In the numerator: U(-4,4)10 = 4*U(-1,1)10 - the 4-fold quartus of 10. In the denominator: U(1,1)10 = - the tertius of 10.