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46 is carréphobic - approach of √46 ~ 6.7823299831

Subsequent approximations of √46 - the position of a fraction indicates whether it is over or under the root-value.
 1 0 1 2 3 4 5 6 7 20 27 34 61 95 156 529 685 841 997 2150 3147 5297 13741 19038 24335 165048 189383 213718 238053 262388 286723 311058 335393 981844 1317237 1652630 2969867 4622497 7592364 25746959 33339323 40931687 48524051 104640466 153164517 257804983 668774483 926579466 1184384449 8032886160 ... 0 1 1 1 1 1 1 1 1 3 4 5 9 14 23 78 101 124 147 317 464 781 2026 2807 3588 24335 27923 31511 35099 38687 42275 45863 49451 144765 194216 243667 437883 681550 1119433 3796182 4915615 6035048 7154481 15428395 22582876 38011271 98605418 136616689 174627960 1184384449 ...

 Diophantine equation: s2-46p2 = 1 d = distance to nearest square N2: -3 Smallest non-trivial s: (2*49-3)/3 rational: 95/3 actual: 24335 ⇒ F=48670 Smallest non-trivial p: 2*7/3 rational: 14/3 actual: 3588 ⇒ primus foldage=3588 v-value tq-blocks: 1562-46*232: +2 v-value qt-blocks: 5292-46*782: -23 Number of series: 24

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
 s 1 24335 1184384449 ... p 0 3588 174627960 ...

 In the numerator: U(1,24335)48670 = 1/2*U(2,48670)48670 - half the secundus of 48670. In the denominator: U(0,3588)48670 = 3588*U(0,1)48670 - the 3588-fold primus of 48670. as well as ... In the numerator: U(0,165048)48670 = 165048*U(0,1)48670 - the 46*3588-fold primus of 48670. In the denominator: U(1,24335)48670 = 1/2*U(2,48670)48670 - half the secundus of 48670. and ... In the numerator: U(156,156)48670 = 156*U(1,1)48670 - the 156-fold tertius of 48670. In the denominator: U(-23,23)48670 = 23*U(-1,1)48670 - the 23-fold quartus of 48670. and ... In the numerator: U(-529,529)48670 = 529*U(-1,1)48670 - the 529-fold quartus of 48670. In the denominator: U(78,78)48670 = 78*U(1,1)48670 - the 78-fold tertius of 48670.