### Who's Online

We have 22 guests and no members online

109 is carréphobic - approach of √109 ~ 10.4403065089

Here Ed's program failed to provide the last 24 fractions before the sp-block. The sp-block itself was derived from the qt-block, after it was identified as such. The positioning of the missing fractions is derived from a property of roots with the qt-block in the middle of the section: corresponding fractions in the first and second half are on opposite sides of the root-value.
Subsequent approximations of √109.
 1 0 1 2 3 4 5 6 7 8 9 10 21 52 73 94 167 261 877 1138 1399 5335 6734 8133 9532 39527 49059 58591 68123 194837 262960 331083 730289 1061372 2853033 3914405 4975777 8890182 101706407 110596589 119486771 128376953 137267135 146157317 155047499 163937681 172827863 181718045 372326272 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 158070671986249 1650306265605900 ... 0 1 1 1 1 1 1 1 1 1 1 1 2 5 7 9 16 25 84 109 134 511 645 779 913 3786 4699 5612 6525 18662 25187 31712 69949 101661 273271 374932 476593 851525 9741707 10593232 11444757 12296282 13147807 13999332 14850857 15702382 16553907 17405432 35662389 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 15140424455100 158070671986249 ...

 Diophantine equation: s2-109p2 = 1 d = distance to nearest square N2: +9 Smallest non-trivial s: (2*100+9)/9 rational: 209/9 actual: 158070671986249 ⇒ F=316141343972498 Smallest non-trivial p: 2*10/9 rational: 20/9 actual: 15140424455100 ⇒ primus foldage=15140424455100 v-value qt-blocks: 88901822-109*8515252: -1 Number of series: 73

Cross multiplying the red-green pairs renders subsequent solutions of the diophantine equation.
 s 1 158070671986249 ... p 0 15140424455100 ...

 In the numerator: U(1,158070671986249)316141343972498 = 1/2*U(2,316141343972498)316141343972498 - half the secundus of 316141343972498. In the denominator: U(0,15140424455100)316141343972498 = 15140424455100*U(0,1)316141343972498 - the 15140424455100-fold primus of 316141343972498. as well as ... In the numerator: U(0,1650306265605900)316141343972498 = 1650306265605900*U(0,1)316141343972498 - the 109*15140424455100-fold primus of 316141343972498. In the denominator: U(1,158070671986249)316141343972498 = 1/2*U(2,316141343972498)316141343972498 - half the secundus of 316141343972498. and ... In the numerator: U(-8890182,8890182)316141343972498 = 8890182*U(-1,1)316141343972498 - the 8890182-fold quartus of 316141343972498. In the denominator: U(851525,851525)316141343972498 = 851525*U(1,1)316141343972498 - the 851525-fold tertius of 316141343972498.