√109

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√109

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.

2	3	5	6	7	8	10	11	12	13	14	15	17	18	19	20	21	22	23	24	26	27	28	29	30
31	32	33	34	35	37	38	39	40	41	42	43	44	45	46	47	48	50	51	52	53	54	55	56	57
58	59	60	61	62	63	65	66	67	68	69	70	71	72	73	74	75	76	77	78	79	80	82	83	84
85	86	87	88	89	90	91	92	93	94	95	96	97	98	99	101	102	103	104	105	106	107	108	109	110

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