[mwhakhoy] factoring binary golden ratio reciprocal

see previous post for explanatory details.

let phi = the golden ratio ~= 1.618.  the number we examine is 1/phi = phi-1 = (sqrt(5)-1)/2 ~= 0.618 (decimal) ~= 0.1001111000110111011110011011100101111111010010100111110000010101110 (binary).

1 floor matrix(0,2)
2 ceil Mat([3, 1])
3 ceil Mat([5, 1])
4 floor Mat([3, 2])
5 floor Mat([19, 1])
6 floor [3, 1; 13, 1]
7 floor Mat([79, 1])
8 ceil [3, 1; 53, 1]
9 ceil Mat([317, 1])
10 ceil [3, 1; 211, 1]
11 floor [5, 1; 11, 1; 23, 1]
12 floor Mat([2531, 1])
13 ceil [61, 1; 83, 1]
14 floor [3, 4; 5, 3]
15 floor [7, 1; 11, 1; 263, 1]
16 floor [3, 1; 23, 1; 587, 1]
17 ceil [59, 1; 1373, 1]
18 floor [19, 1; 8527, 1]
19 floor [3, 3; 11, 1; 1091, 1]
20 floor [5, 1; 31, 1; 37, 1; 113, 1]
21 floor [3, 1; 432037, 1]
22 ceil [29, 1; 89387, 1]
23 ceil [5, 1; 7, 3; 3023, 1]
24 floor [19, 1; 545731, 1]
25 floor [3, 1; 6912593, 1]
26 ceil [41, 1; 1011599, 1]
27 floor [353, 1; 234989, 1]
28 floor [3, 1; 5, 1; 17, 1; 31, 2; 677, 1]
29 floor [337, 1; 984583, 1]
30 ceil [3, 5; 29, 1; 94169, 1]
31 ceil [5, 1; 7, 1; 37920511, 1]
32 floor [3, 1; 89, 1; 523, 1; 19009, 1]
33 ceil [54493, 1; 97423, 1]
34 floor [19, 1; 558828583, 1]
35 floor [3, 1; 5, 1; 13, 1; 2621, 1; 41549, 1]
36 floor [103, 1; 251, 1; 1642787, 1]
37 floor [3, 4; 43, 1; 811, 1; 30071, 1]
38 floor [613, 1; 2237, 1; 123887, 1]
39 floor [3, 1; 5, 1; 22651185233, 1]
40 floor [17, 1; 23, 1; 229, 1; 7589269, 1]
41 ceil [3, 1; 11, 1; 41183973151, 1]
42 floor [5, 1; 283, 1; 463, 1; 4148917, 1]
43 ceil [7, 1; 181, 1; 2089, 1; 2053937, 1]
44 ceil [3, 2; 83, 1; 569, 1; 25579927, 1]
45 floor [13, 1; 29, 1; 311, 1; 6367, 1; 29129, 1]
46 ceil [53, 1; 2267, 1; 361963493, 1]
47 floor [3, 1; 5, 1; 103, 1; 25913, 1; 2172581, 1]
48 ceil [7, 1; 24851586084253, 1]
49 ceil [47, 1; 67, 1; 56533, 1; 1954373, 1]
50 floor [19, 1; 31, 1; 173, 1; 6828899873, 1]
51 floor [3, 3; 11, 2; 17, 1; 18191, 1; 1377487, 1]
52 floor [13, 1; 1361, 1; 157315189139, 1]
53 floor [3, 1; 5, 1; 41, 1; 43, 1; 449, 1; 13163, 1; 35617, 1]
54 floor [547, 1; 20353767030613, 1]
55 ceil [3, 1; 29, 3; 31, 1; 37, 1; 241, 1; 1100947, 1]
56 ceil [5, 1; 13, 1; 83, 1; 18979, 1; 434937989, 1]
57 ceil [3, 1; 73, 1; 406703582310331, 1]
58 ceil [1559, 1; 3023, 1; 191137, 1; 197753, 1]
59 ceil [3, 2; 137, 1; 288947557261841, 1]
60 floor [5, 1; 31, 1; 113, 1; 8929, 1; 4556161763, 1]
61 ceil [7, 1; 7621, 1; 3922081, 1; 6811073, 1]
62 floor [3, 1; 23, 1; 283, 1; 2687, 1; 54321142829, 1]
63 ceil [13, 1; 10400389, 1; 42160829899, 1]
64 floor [5, 1; 139, 1; 199, 1; 82431689521877, 1]
65 floor [3, 1; 41, 1; 1753, 1; 5147, 1; 5333, 1; 3852559, 1]
66 floor [37, 1; 213359, 1; 5776694258021, 1]
67 floor [3, 2; 11, 1; 143177, 1; 875327, 1; 7350947, 1]
68 floor [5, 2; 17, 1; 80611, 1; 5324377336013, 1]
69 ceil [3, 1; 2617, 1; 10103, 1; 350429, 1; 13125223, 1]
70 ceil Mat([729645748436684703101, 1])
71 floor [3, 2; 29, 1; 47, 1; 6727703, 1; 17682223501, 1]
72 floor [7, 1; 13, 1; 32072340590623503433, 1]
73 floor [3, 1; 131, 1; 14852839662833276399, 1]
74 ceil [5, 1; 2334866394997391049923, 1]
75 ceil [467, 1; 432389, 1; 115629997708483, 1]
76 floor [557, 1; 6469, 1; 12959841314715929, 1]
77 floor [3, 1; 5, 1; 11, 1; 75629, 1; 7484274775140019, 1]
78 floor [13, 1; 17529228919, 1; 819682865173, 1]
79 ceil [3, 2; 61, 1; 1626617, 1; 418335158497211, 1]
80 ceil [5, 2; 19, 1; 1572962623998242391527, 1]
81 floor [3, 1; 54543282077, 1; 9132285626479, 1]
82 floor [91291, 1; 924389407, 1; 35415149527, 1]
83 ceil [3, 4; 41, 1; 3644437, 1; 493858663895587, 1]
84 ceil [11, 1; 13, 1; 481157, 1; 2742521, 1; 63351833407, 1]
85 ceil [3, 1; 59, 1; 135079276185159798594409, 1]
86 ceil [5, 1; 29063, 1; 354454423, 1; 928370091293, 1]
87 ceil [3, 1; 37, 1; 73, 1; 9592753, 1; 1230361920924391, 1]
88 ceil [23, 1; 449, 1; 1031, 1; 17964665531981628001, 1]
89 ceil [3, 2; 14827, 1; 2866725944083785208811, 1]
90 floor [5, 1; 10382612797, 1; 14737889879391697, 1]
91 floor [7, 1; 995023, 1; 219690261377373789131, 1]
92 ceil Mat([3060356081250980396954930183, 1])
93 ceil [3, 1; 5, 1; 172724254517, 1; 2362421413490423, 1]
94 ceil Mat([12241424325003921587819720729, 1])
95 ceil [3, 1; 109, 1; 823, 1; 3343, 1; 27213097856682744319, 1]
96 ceil [55138902187, 1; 888042658773867299, 1]
97 ceil [3, 2; 5, 2; 3440051, 1; 126524473813558607387, 1]
98 floor [19, 2; 107, 1; 179, 1; 773, 1; 2677, 1; 61323517, 1; 223230229, 1]
99 ceil [47, 1; 429673, 1; 19397511071141903549029, 1]
100 floor [3, 1; 17, 1; 191, 1; 80428206221152959821421017, 1]
101 floor [5, 1; 677, 1; 1277, 1; 61589584627, 1; 5885523205733, 1]
102 floor [3, 2; 27941, 1; 12461991844724415043133939, 1]
103 ceil [13, 1; 163, 1; 271, 1; 91283, 1; 7424240093, 1; 16104963793, 1]
104 ceil [5, 1; 61, 1; 313, 1; 131306955520913588288141141, 1]
105 floor [11, 1; 19, 1; 119954244103387710104568363881, 1]
106 floor [3, 1; 7, 2; 17, 1; 419, 1; 541, 1; 1471, 1; 195734741, 1; 307421167589, 1]
107 floor [151, 1; 293, 1; 54287, 1; 155065539073, 1; 269256497683, 1]
108 ceil [3, 1; 67, 1; 174084923, 1; 5731848122248213775893, 1]
109 floor [181, 1; 1289, 1; 4723, 1; 11681459, 1; 31162720200181529, 1]
110 floor [5, 1; 53, 1; 91926797484623, 1; 32932437651392749, 1]
111 ceil [11, 1; 62540347, 1; 492331109, 1; 4737308072003987, 1]
112 floor [3, 1; 43, 1; 2606760735653, 1; 9542913626237275433, 1]
113 floor [7, 1; 7468840733, 1; 122758233763498148898353, 1]
114 floor [3, 1; 1361, 1; 3143782452367208445473830879789, 1]
115 ceil [5, 2; 58907, 1; 2691633979283, 1; 6476478744889159, 1]
116 ceil Mat([51344255012061248331478605928713949, 1])
117 floor [13, 1; 4133, 1; 1911230620784352894395153675993, 1]
118 ceil [3, 4; 5, 1; 23549, 1; 67752082954261, 1; 317834987971751, 1]
119 ceil [29, 1; 31, 1; 97, 1; 54841926536539, 1; 85889033379678517, 1]
120 ceil [3, 1; 11, 1; 911, 1; 1620461, 1; 3056897, 1; 5516455683519795587, 1]
121 ceil [59, 1; 629281, 1; 44253253366882875573635312707, 1]
122 ceil [3, 1; 5, 1; 98507, 1; 18507701, 1; 120160300031889420428921, 1]
123 floor [991, 1; 2719, 1; 4253, 1; 12979, 1; 113036977589, 1; 390896527547, 1]
124 floor [7, 4; 29, 1; 35839, 1; 60077, 1; 251417, 1; 21678401, 1; 16086281261, 1]
125 ceil [43, 1; 73, 1; 577, 1; 33303089, 1; 435823025136719782515517, 1]
126 floor [3, 4; 13, 1; 37, 1; 1349465289195624298437773477862557, 1]
127 ceil [5, 1; 21030606852940287316573636988401233311, 1]
128 ceil [75377, 1; 2790056231070523809195595073882117, 1]
129 ceil [11, 1; 17, 1; 653, 1; 1109, 1; 5921479, 1; 15352291, 1; 34165838150667247, 1]
130 ceil [211, 1; 3986844901031334088449978576000233803, 1]
131 ceil [5, 1; 541309, 1; 1213271, 1; 23335673, 1; 21955755812132032559, 1]
132 floor [157, 1; 1327, 1; 16151066754042430705013376843242011, 1]
133 ceil [3, 1; 691, 1; 887, 1; 1319, 1; 1321, 1; 182627, 1; 12811481, 1; 897773797876393, 1]
134 ceil [29, 1; 347, 1; 8179, 1; 163532508199708554320364266225321, 1]
135 ceil [3, 2; 11, 1; 2659, 1; 102260577842218984752429353121867713, 1]
136 ceil [5, 1; 151, 1; 647, 1; 21169, 1; 1234914491174339, 1; 4216026266426479, 1]
137 floor [3, 1; 2837, 1; 1823431, 1; 6938280305108659611823947537769, 1]
138 ceil [5104706001932082773, 1; 42187231564873534102583, 1]
139 ceil [11, 2; 3067, 1; 2056147, 1; 564453863932675759204369896973, 1]
140 ceil [191413, 1; 78519803, 1; 345917718347, 1; 165686953921590301, 1]
141 ceil [5, 1; 7323469, 1; 49622497, 1; 53181773599, 1; 17828444995967279, 1]
142 ceil [547, 1; 43310076029237, 1; 145443886663193360797636511, 1]
143 floor [18199, 1; 689071, 1; 4028429, 1; 136412613088127449222408877, 1]
144 ceil [3, 1; 5, 1; 7, 1; 241, 1; 733, 1; 26161, 1; 28403187337858238166159216355111, 1]
145 ceil Mat([27565237014285893391579397473437264525140229, 1])
146 ceil [3, 1; 11600897809, 1; 1584086419753979542566132174631891, 1]
147 floor [7, 2; 59, 1; 2903, 1; 2969, 1; 4425031812254529290260215725955949, 1]
148 ceil [1487, 1; 44753, 1; 3313741266236597486165003929098299357, 1]
149 ceil [3, 1; 19, 1; 220609661, 1; 16264705842883, 1; 2156433736359084105083, 1]
150 floor [5, 1; 524429, 1; 336399239728218152897929259880743614409, 1]
151 floor [418637, 1; 498688674404337283, 1; 8450347921735757415541, 1]
152 floor [7, 1; 3299, 1; 1823669, 1; 3657865064074471, 1; 22904332979088548489, 1]
153 ceil [29, 1; 1021, 1; 26352788611, 1; 399324131917133, 1; 22647789601969841, 1]
154 floor [3, 1; 433, 1; 3319, 1; 103348937, 1; 1027948379, 1; 86464944701, 1; 356367344111, 1]
155 floor [17, 1; 59, 1; 61, 1; 70141, 1; 36762419, 1; 82009493, 1; 2181678534758789635687, 1]
156 ceil [3, 1; 5, 2; 7, 1; 79, 1; 1361147809650572867171901290550922670222717, 1]
157 floor [19, 1; 194218099297, 1; 44238501634169333, 1; 691636603703978371, 1]
158 ceil [53, 1; 4260649464547736578562611775516944735659410383, 1]
159 floor [3, 2; 41, 1; 617, 1; 1549, 1; 293261, 1; 103063807201, 1; 42369977156879313806101, 1]
160 floor [5, 1; 163, 1; 3178963, 1; 348633073067480225684072893867426325831, 1]
161 floor [3, 1; 13, 1; 46320906999185648956680702379979091485117692369, 1]
162 floor [3248579767, 1; 863436343056517, 1; 1288094712679373010004597, 1]
163 floor [3, 1; 835733, 1; 2882125228939929075132125360323108884328033, 1]
164 floor [5, 1; 307, 1; 8291, 1; 1135576388018240608177571704065393033877771, 1]
165 ceil [3, 3; 11, 1; 1201023550553279, 1; 2789433132956641, 1; 29049436767644537, 1]
166 ceil [7, 1; 17, 1; 89, 1; 107, 1; 281, 1; 181536757613041728280850438867418570980753, 1]
167 floor [3, 1; 193, 1; 3187, 1; 1715887, 1; 13999203637, 1; 2608368780681571000596002963, 1]
168 floor [29, 1; 463, 1; 497877068508427, 1; 34589996543494362818915486541347, 1]
169 floor [3, 2; 181, 1; 283, 1; 2587649, 1; 2601472042891, 1; 149021722058183254652690779, 1]
170 ceil [5, 1; 19, 1; 4348820697553761360409, 1; 2238806274126396968960347961, 1]
171 floor Mat([1849871741919478076734000530246844997549660162449309, 1])
172 ceil [3, 1; 31, 1; 41, 1; 43, 1; 199, 1; 72139, 1; 36428381825992568521, 1; 43149252731364815561, 1]
173 ceil [127, 1; 233, 1; 499, 1; 127297, 1; 71304346259, 1; 55208665654065339078649544891, 1]
174 ceil [3, 2; 97, 1; 3269872440041300976293, 1; 5184257333824972128307856557, 1]
175 floor [5, 1; 23, 1; 257373459745318688936904421599561043137344022601643, 1]
176 ceil [523, 1; 2593, 1; 3240321438083, 1; 13470983272672265519085740946521443, 1]
177 ceil [3, 1; 17, 1; 64151, 1; 374124162161698969907, 1; 96723550092825425146369483, 1]
178 floor [73, 1; 347, 1; 134033, 1; 4955999, 1; 14072015494242611823531395658769175293, 1]
179 floor [7, 1; 107, 1; 483081013, 1; 1308819622601636146216814004984440128151779, 1]
180 floor [31, 1; 3581999772187003, 1; 8529514887159251514594939660695236379, 1]
181 ceil [5, 1; 11, 1; 34441248431373555465011209872232168681651854660874409, 1]
182 ceil [3, 3; 373552661239703734900397093, 1; 375626282107957869342241499, 1]
183 floor [29, 1; 109, 1; 151, 1; 2066899, 1; 4889741863, 1; 1023663809471, 1; 1534396452641022457541, 1]
184 ceil [5, 1; 23, 1; 61, 1; 6133, 1; 12907, 1; 222533, 1; 7655897, 1; 250924027, 1; 63837057186230464795181, 1]
185 ceil [3, 1; 11, 1; 13, 1; 2711729, 1; 39880672292023, 1; 653274203249875295546802389338463, 1]
186 floor [677, 1; 89537071254383246112879954763853200708577938261652821, 1]
187 ceil [5, 1; 7, 1; 41, 1; 1055626473529, 1; 80031208455657530851037431832468903747249, 1]
188 floor [3, 4; 2617, 1; 699855853, 1; 1634384383741664010475436791844290146453649, 1]
189 ceil [1058153, 1; 4218404987, 1; 108638760249643698815726940628051462767049, 1]
190 ceil [11, 1; 653, 1; 173539, 1; 85656259692230527, 1; 9083421609734893098541373024023, 1]
191 ceil [7, 1; 17, 1; 59, 1; 45233, 1; 324799, 1; 11954325067, 1; 641882633927233, 1; 2450709280140666089, 1]
192 floor [5, 1; 3167, 1; 4463, 1; 58960204966363, 1; 931038388342686372796393382876338007, 1]
193 floor [3, 1; 79, 1; 13689740219, 1; 38846091546697, 1; 61561705173508223782062272518421, 1]
194 floor [109, 1; 127, 1; 197, 1; 743719187, 1; 7651138923698712545420223408883449417318499, 1]
195 floor [3, 1; 39779, 1; 142787, 1; 661187926723, 1; 27068271264562603, 1; 101768247158729041277, 1]
196 floor [5, 1; 11, 1; 26783, 1; 23159867, 1; 1819422403241810849615355735808121750159248549, 1]
197 floor [3, 2; 577, 1; 34922659868258902457, 1; 684535331769683290274410092532718591, 1]
198 ceil [103, 1; 2046597577207, 1; 1177827854751485158844033077807969366880064223, 1]
199 ceil [5, 1; 181, 1; 90686569, 1; 106594022196783856849, 1; 56761922488479000995461638653, 1]
200 ceil [7, 1; 23, 1; 458300458060230405467, 1; 13459698298269268563405071101030277467, 1]
201 ceil [112657, 1; 7882629823, 1; 2236722848233170057637190860387281943495169887, 1]
202 floor [11, 1; 1873, 1; 34961, 1; 158699, 1; 34752254558865556029429834889533097353604021289, 1]
203 floor [3, 1; 5441, 1; 213737, 1; 333634231993, 1; 25465172134442075251, 1; 268043061117968490139, 1]
204 ceil [5, 1; 619, 1; 215653, 1; 23807583584907237047146473103722484684943826308396093, 1]
205 floor [43, 1; 12637566484849, 1; 58482989146088169168870285991543162331458523287, 1]
206 floor [3, 2; 11, 1; 19, 1; 727, 1; 2016414986888774979530539, 1; 23050924246008467923375086268783, 1]
207 ceil [17, 1; 4093, 1; 1826967392440743445471956026767504478902456827842963968019, 1]
208 ceil [7, 1; 269, 1; 709, 1; 36923, 1; 56617069, 1; 687369903301634207, 1; 132531778862952771804480299, 1]
209 ceil [2003, 1; 16787, 1; 36313, 1; 416452318392996075756645382089473779785776113860121, 1]
210 floor [5, 1; 31, 1; 1249, 1; 79243756499353, 1; 358244245542796297, 1; 185043159336978853006425059, 1]
211 floor [3, 1; 59, 1; 107, 1; 227, 1; 473106095580852766782235188367605355367485078249194763187, 1]
212 ceil [13, 1; 617, 1; 1847, 1; 274584506700597168878654381838382916520391359877163325229, 1]
213 floor [5, 1; 17, 1; 53, 1; 104587907, 1; 11672034271, 1; 820022417716721, 1; 1804067943172208918992913897, 1]
214 ceil [3, 2; 41, 1; 67, 1; 73, 1; 9015865056651079893416963547453314411766491416889316259729, 1]
215 floor [37, 1; 32633, 1; 17785791301468736007953209547, 1; 1515407772766896909609093637163, 1]
216 ceil [565463, 1; 345217162409702458068671, 1; 333422460265130042393898941308138931, 1]
217 ceil [3, 1; 5, 3; 83, 1; 109, 1; 463, 1; 653153, 1; 126878969831918659161064076926746233496304411651627, 1]
218 ceil [7272833, 1; 35797096226084507798182466841648629260709858978765679475753, 1]
219 ceil [3, 1; 17, 1; 7451, 1; 1544119, 1; 19718911, 1; 716900914423723, 1; 62773138465612828706582018918971, 1]
220 floor [1567, 1; 664572566017212173843979029655004276431541201802459050309327679, 1]
221 ceil [43, 1; 11610335663, 1; 637869401093, 1; 6540280893405396064933365742756115376487451, 1]
222 ceil [3, 1; 41, 1; 79, 1; 56929, 1; 58616096532337637285537, 1; 128466160809916607642552046652387153, 1]
223 ceil [5, 1; 53, 1; 191, 1; 4202483, 1; 39166628288648861928274427323821793973048968646485554821, 1]
224 floor [3, 2; 5303, 1; 659609, 1; 529274144932433995528937771396767014443805062057885297623, 1]
225 floor [11, 1; 3967, 1; 39541, 1; 40813, 1; 3083023331951, 1; 1715825681305218103, 1; 89456181407597429017183, 1]
226 floor [3, 1; 149, 1; 359, 1; 1931, 1; 253229, 1; 4720323403, 1; 179937606774057684125014577051349848690963539, 1]
227 ceil [67, 1; 236836949, 1; 37945900228123361, 1; 183747972839828629, 1; 1204785405732032075448397, 1]
228 floor [23, 1; 97, 1; 2351, 1; 50827549470243967245093045408481637461664675185275509177015077, 1]
229 ceil [3, 2; 5, 2; 11, 1; 13, 1; 1910009, 1; 454191861291191, 1; 1412438764944049, 1; 13524412901405182976712747067, 1]
230 ceil [181906739569, 1; 881918510247889, 1; 25841730997479797, 1; 257224607619624555247379137, 1]
231 ceil [3, 1; 19, 1; 356219, 1; 105038720366506922815758421705852555024056752860128495938433859, 1]
232 ceil [139619, 1; 23454159388067, 1; 1302587656754405632337974833343120198322970334792841, 1]
233 floor [3, 1; 5, 1; 29, 1; 919, 1; 226314268199, 1; 94294127376890145730957699924619004059012646458456411, 1]
234 floor [181, 1; 94265498873966567235132773729649246585304969258947201042983396096791, 1]
235 ceil [3, 1; 373, 1; 30495183728664787613152872287875806312672385050704992651974968174297, 1]
236 ceil [5, 1; 7, 1; 19, 1; 47, 1; 2183593702919590295256315091353897121348929699039442442972963646587, 1]
237 ceil [3, 1; 11, 1; 98869, 1; 41835720290271942137230334587374756696884673379239056489575878197, 1]
238 ceil [103, 1; 15492259019062649455217, 1; 171080044132243798306991687846308112580016187287, 1]
239 ceil [3, 2; 7, 1; 97, 1; 11972065403, 1; 339159632849, 1; 2736600675172478929, 1; 8040524373809360125112650861, 1]
240 floor [5, 1; 429583503031, 1; 508386160665591881422230177802619759765200620905611582873819, 1]
241 floor [37, 2; 1447, 1; 1102476486154350443048364390983745491358583022222895234120234313037, 1]
242 ceil [17, 1; 19, 1; 3083, 1; 4001, 1; 8639713, 1; 537383656981, 1; 236125527712310616577600171884917454394410379, 1]
243 ceil [3, 1; 5, 1; 1504961, 1; 3665491, 1; 1554624791, 1; 491770032710019985969687, 1; 138090879169509845457153313, 1]
244 ceil [7, 1; 1283, 1; 596159, 1; 759659, 1; 5744561, 1; 18358095920860931731, 1; 40732525024415635917176726796779, 1]
245 floor [3, 1; 83, 1; 11831, 1; 17124048877875166831, 1; 692682215244057923589958432639627255023761735713, 1]
246 floor [5, 1; 333748937, 1; 41879491285502334199502661041639476344715403177042172943575762319, 1]
247 floor [3, 1; 11, 1; 31, 1; 907, 1; 2749, 1; 26891, 1; 6065241421575631, 1; 335976253692766797219973170670396132210153499, 1]
248 ceil [43, 1; 276546000786426297673, 1; 9719305382560385649127, 1; 2418690052652268070673197030771, 1]
249 floor [5, 3; 1699, 1; 9576518112642642559449613534847977, 1; 274897160432925077894640948182039603, 1]
250 ceil [3, 1; 13, 1; 113, 1; 12544967, 1; 147681235818824631192197457037, 1; 136953578350798246703747380030924967, 1]
251 ceil [23, 1; 107, 1; 12783253489, 1; 1676040549457, 1; 2478642158129, 1; 43382108189836523, 1; 394438455829116564251, 1]
252 floor [3, 1; 454186924603914318885906889, 1; 3282580498080493336684403341974619611720947221003, 1]
253 ceil [17, 1; 4943, 1; 245497986763, 1; 2778444900761729, 1; 156067332391269649784166983258824741202746919, 1]
254 floor [5, 1; 7, 2; 251, 1; 4919, 1; 95582609, 1; 296199191, 1; 30210769235960982247009657, 1; 69149667739088349341389787, 1]
255 ceil [3, 2; 6026681618489012541696473, 1; 659690903692485105644246488354183258003118502665323, 1]
256 floor [111329016410357275229789624799047672243, 1; 642810374909272385191274692085412420247, 1]
257 ceil [157, 1; 47491, 1; 19195979547186694000895141471055973030492081504592140591528367859174989, 1]
258 ceil [3, 1; 5, 1; 71, 1; 151, 1; 2753, 1; 877463, 1; 867555420443, 1; 849361232193747693366163899027094553736695552751367, 1]
259 floor [47, 1; 318147281887, 1; 38287337063253510981248789923884104374997503305612474906055627321, 1]
260 ceil [11, 2; 31, 2; 431, 1; 22846790758397002686456089248321008253648557277665889363282248847266949, 1]
261 ceil [3, 2; 89, 1; 2495604120292402841, 1; 1145600034326988237262225948845062523785636016329229131597, 1]
262 floor [13, 1; 12956089203946367, 1; 46116297454220897, 1; 589657070043660756699799229600367020213677619, 1]
263 floor [7, 2; 503, 1; 50461, 1; 5038063, 1; 92641983163, 1; 15780104111810661967978257008667310667677164593445109, 1]
264 floor [5, 1; 3323, 1; 5937683, 1; 1157496669257, 1; 41070220930753853, 1; 3906313302067307821920951915298098822847, 1]
265 ceil [19, 1; 919, 1; 2098418461132547763732969285120459143059427799231914228295443861970058493171, 1]
266 floor [3, 1; 13, 1; 137, 1; 68699, 1; 3612023, 1; 55271991095177328146224927182721598190187415804215576263586884751, 1]
267 floor [933019, 1; 134965309, 1; 3385227161, 1; 343811773147034203139302562267219627246882543679265084733, 1]
268 ceil [3, 3; 73, 1; 38041125429265266192710753222461, 1; 3909409973307263784423731560756272608736828337, 1]
269 ceil [11, 1; 677, 1; 7218311, 1; 264270513827, 1; 228205446395812021883, 1; 180837933516475272185934083570528855869, 1]
270 floor [3, 1; 5, 1; 17, 1; 757, 1; 90710167, 1; 2829709745128644193, 1; 236457133801450838513, 1; 100074827720030966440728138877, 1]
271 floor [239, 1; 2473, 1; 281150417, 1; 24665479647043937771, 1; 572124927212862206149090580396238834365310893999, 1]
272 floor [3, 2; 13, 1; 31, 1; 959415441331800689051771, 1; 1347773524293711375808830286088379131707845886495291279, 1]
273 floor [607, 1; 26885533135353322311919, 1; 574769655790839596927203178843308807576708752571659693439, 1]
274 floor [3, 1; 5, 3; 761, 1; 8758819, 1; 664194283, 1; 26965231180035344752879, 1; 419054408950176560902154474325629972239, 1]
275 floor [97, 1; 229, 1; 43579, 1; 485753, 1; 8312599, 1; 251255333547486195771413, 1; 38204021318618349250365232812920131483, 1]
276 floor [3, 1; 1297, 1; 47824807285738823740342012703, 1; 403252161101333343030146851454229121328835926382811, 1]
277 ceil [31, 1; 857, 1; 4522880773, 1; 1249003062919252141030653635215857072375352500452436957836757340602677, 1]
278 ceil [7, 1; 19, 1; 101, 1; 61283, 1; 65336352619211, 1; 5580630082823495778829454720436293894166838595764367017365797, 1]
279 ceil [5, 2; 29, 1; 4603, 1; 13672126747, 1; 61690003891, 1; 213280571137578625866886731696934107098566731975126986639, 1]
280 ceil [4748020658364559071646243549, 1; 252870720384810215559359637651416792917747763315137150501, 1]
281 floor [7, 3; 13, 1; 157, 1; 641881, 1; 3241743041, 1; 118757300293, 1; 13880675215469993702827406501062805702198541911577323, 1]
282 ceil [3, 2; 5, 1; 23, 1; 22649680387909902209911183, 1; 204865443956647796037512638895362099481654083208853995719, 1]
283 floor [38829874003, 1; 1722336896444640338953819307, 1; 143620702288944504724643854844232076617255489109, 1]
284 floor [10781, 1; 20517090403261320881, 1; 191087831338491454271, 1; 454488897578435065087076026691041955032009, 1]
285 ceil [7, 1; 950539823, 1; 226102536581, 1; 22926648157628407928123860027739, 1; 1113901443649022073508361989145641, 1]
286 ceil [3, 1; 11, 2; 13, 1; 107, 1; 271, 1; 19219, 1; 50033, 1; 7068245491, 1; 1080949503648317, 1; 76433493762703045237115930250764422901380651, 1]
287 ceil [59, 1; 137, 1; 2014027, 1; 3735480207957561082239917616798063761, 1; 2527183680581155133667978950489294479033, 1]
288 floor [3, 1; 5, 1; 7, 2; 3255675529, 1; 236160769181, 1; 62796175095946205254651, 1; 8661272654687678491649749681360726234681, 1]
289 ceil [2287, 1; 49867453209947, 1; 532624082681651771, 1; 10119917078203205276760872475416019538820249379653749, 1]
290 floor [11, 1; 47, 1; 4439833, 1; 43319371, 1; 44220625997, 1; 278972541235412440616791, 1; 1002271630013540865172977043838425553, 1]
291 ceil [3, 2; 136393, 1; 1867813, 1; 17287603, 1; 61809264592343, 1; 74310568148475548602462927, 1; 13506231023897153294902914701, 1]
292 floor [5, 1; 19, 1; 317, 1; 1087, 1; 1593123162795424882651, 1; 94299486984018706683421498681983119202449674943899426834139, 1]
293 ceil [31, 1; 317277588125261804961600632579796814945301720775294149353699449329814093859017726163061, 1]
294 ceil [3, 1; 7, 1; 379, 1; 7173433, 1; 344544668425126455729671449752102568539622681799428295189994830860954174413323, 1]
295 floor [5968589530429, 1; 183499362763890701651, 1; 35921528444573415265929826046277120232123156251380690959, 1]
296 floor [43, 1; 487, 1; 1297, 1; 2058802307349534911, 1; 1407145600263522606875801908073936101202102884431230860416334609, 1]
297 floor [2239, 1; 6131, 1; 163993, 1; 5735825840065606040800151519099109479, 1; 12187493453010668477089899681314317883789, 1]
298 floor [5, 1; 62947873484051942104381565503831688085147861401818359231773970747035116221629116870751299, 1]
299 ceil [13, 1; 67, 1; 14880073517760631, 1; 169723713284239004713285536373141, 1; 286164203424111691986369403499627661251, 1]
300 floor [3, 1; 23, 1; 87719, 1; 192667, 1; 221728139881291509023, 1; 4869004180585303426091559020803244909919572530607584446131, 1]
301 ceil [515555489288779553, 1; 4883887363580588072098116905541551806234152814038011544280871250922002971, 1]
302 ceil [5, 2; 47, 1; 2789, 1; 33469, 1; 21385591, 1; 2146943800130444928451220261088740469748469930544908492360129337325662901, 1]
303 floor [1229, 1; 186437, 1; 520212887, 1; 104431080562010491, 1; 8148479328535971097815161, 1; 99295509964891331992511220692149, 1]
304 ceil [3, 1; 13, 1; 17, 1; 46483447739, 1; 365295158513, 1; 1789267461306801346500542145934890587487248580515671378953246385039, 1]
305 ceil [7, 1; 19, 1; 31, 1; 241, 1; 4243, 1; 65899, 1; 145003606409622086422229216001693121203028161534125612437617407288815401644447, 1]
306 floor [3, 1; 14150413, 1; 55037593114711052057, 1; 34485873391488153920389268296614384053941412205527635849381074791, 1]
307 floor [103, 1; 20233, 1; 77325639848758551125608413290893671972960891626461912713653588659308328615978481366413, 1]
308 floor [3, 1; 5, 2; 11, 1; 1539546547429080971021, 1; 253748948686890792973902371217865631152218859632707158850397658065179, 1]
309 floor [17, 1; 53, 1; 1602911042783834685968083, 1; 446320472410697443357354974649959222638967653021398689498569122897, 1]
310 ceil [3, 4; 287783, 1; 28579927, 1; 940761151261, 1; 4854747312640560459060803, 1; 423695392277847143596023093458211714190121, 1]
311 floor [5, 1; 4397, 1; 104307353, 1; 1712949713, 1; 7549301717, 1; 258841986511685411, 1; 15042681490358405440357, 1; 22329974967930016037423, 1]
312 floor [11, 1; 158545437301267, 1; 24082377765818265183912048254447, 1; 122779315806016644856021043349513751818449677349, 1]
313 ceil [367926263, 1; 84836458288440624791, 1; 330413424165460612909824584851903470017887176515167979217672008231, 1]
314 floor [3, 1; 5, 1; 19, 2; 163, 1; 191, 1; 6267486401748101, 1; 19521723859738705171510366355014234415797708235037697667903453591918491, 1]
315 floor [23, 1; 151, 1; 2683, 1; 3288246991, 1; 863331649435547, 1; 1559528961330418748094061434137009571980238251492202964947253837, 1]
316 floor [3, 2; 14753, 1; 155863, 1; 2597427544585977338629619, 1; 62640187529973146172187067, 1; 24503527850702728296849657005227321, 1]
317 floor [739, 1; 13807, 1; 125441, 1; 3283422654039427, 1; 161227910701165265690440048157, 1; 243540222269022693741300426793323688621, 1]
318 floor [3, 1; 5, 1; 2927, 1; 30803, 1; 4818071107784309, 1; 28181661845663493811262361511, 1; 1797232149618147849665226501563547630768391, 1]
319 floor [961397445270373, 1; 686559234280579362877646258169679564621278212620361212128415121275504282921708627, 1]
320 floor [3, 1; 4948835575264328359607513149137581, 1; 88917387241998155869227878419977777558759765110285734097421001, 1]
321 ceil Mat([2640225175456529969761760177189832646622880156690923513992664926001723761088438914074596566431487, 1])
322 ceil [8926271, 1; 214291067, 1; 530857589913613, 1; 60211535216525424945931, 1; 86365262394438709682557601522012630647840663, 1]
323 ceil [5, 1; 29, 1; 1129, 1; 7109790026693, 1; 226771881873728431039147, 1; 40012255750340607705548499845310038843293550677250706599, 1]
324 ceil [61, 1; 10191631, 1; 31109989, 1; 83171232503503, 1; 13130595838726245337541620697433679783953082698971339811422270156737, 1]
325 ceil [68313765677, 1; 587586800447819366789808796146126553, 1; 1052399646633586347323635356720013709945824711746317, 1]
326 ?
327 floor [5, 1; 71, 1; 599, 1; 14891, 1; 127761214727, 1; 5072149880299423642333, 1; 454366973817425207463571, 1; 181235819324373208947657273370199, 1]
328 floor [3, 3; 19, 1; 29, 1; 233, 1; 1319, 1; 1598647199650461881, 1; 37899686173347226854967722777703, 1; 1219962869715238769959575749804997804463, 1]
329 ceil [13, 1; 4843209649096281367, 1; 10735055944102795920720608939299137705693551276142196985686332300351792997931413, 1]
330 floor [5, 1; 241, 1; 185267, 1; 43526039, 1; 293387644139, 1; 16518809124673625933751167, 1; 28704904825609757592456693864131982477425412161, 1]
331 ceil [3, 1; 7, 1; 45063893764551119, 1; 2856886030049804909437486340474071785831720794029179460864766155626146213429619809, 1]
332 ceil [11, 1; 23, 1; 397, 1; 76147, 1; 18630252435257, 1; 37947953071322351674676518879752758711470564215118433460283418239064606710279, 1]
333 ceil [3, 2; 755861, 1; 112851660949149289479969215891, 1; 5669180602590260968246455511019, 1; 2484781590798089923715543630060141, 1]
334 floor [7, 1; 82241, 1; 766177, 1; 3477958734557, 1; 51275649037244624110763, 1; 274966501008116273064668309326401758270566443382028569, 1]
335 floor [4511938049836236513995899711, 1; 9587332272048780009053315382391459738522264985466521631863133578643782813, 1]
336 floor [17, 1; 1567, 1; 71257, 1; 8068071023239205132873, 1; 14947868737041934818174540487, 1; 377917029881235928546508364845507408103119, 1]
337 ceil [5, 2; 7, 1; 4217, 1; 38437489631, 1; 38490195199, 1; 39105714494565633486083992529477, 1; 4052601436574629298622568672778241336975541, 1]
338 ceil [3, 1; 19, 1; 173, 1; 193, 1; 269, 1; 1901, 1; 14153, 1; 122905571, 1; 1578114646709, 1; 14893696321640362405411, 1; 8697152974647395451119807895160246819946621, 1]
339 ceil [13, 1; 1229, 1; 12638551, 1; 58000579297, 1; 66928684064239, 1; 882965535128363657093471943509564834750802519273027904689073620217, 1]
340 ceil [3, 1; 7, 1; 11, 1; 47, 1; 73, 1; 11939, 1; 1106048113, 1; 134335830265555255840409676198277811, 1; 984564907647274689905536720213024209464189060569, 1]
341 ceil [5, 1; 122533, 1; 93067432811, 1; 130961494262091291302116309216337235516031, 1; 370745982968908875024708547875552000486171269, 1]
342 floor [3, 2; 23, 1; 1249, 1; 46527293, 1; 460288693853017940504124592587371087108286223665237090841672543310884279771618775197105531, 1]
343 ceil [13, 1; 2833, 1; 4681940398151, 1; 7581253787160663359, 1; 8471182336752437996431771239820185140564430023146223515047462757399, 1]
344 ceil [11, 1; 75064922879, 1; 863970086017, 1; 6004596744498127, 1; 2021744100520552378829, 1; 2557363153132759575766291958455275690349403, 1]
345 ceil [577, 1; 1386890194798974265943, 1; 55353230611522439149400704323700010049189966876016159862049424277984966943693023, 1]
346 floor [5, 1; 17, 1; 47, 1; 1966954799, 1; 211568697833, 1; 575321796986670911029, 1; 122925134015341599917588957209, 1; 753488735690277684052143270617, 1]
347 ceil [3, 1; 13, 1; 97, 1; 46836508651622629567186380156396611489551922739537371434030094506111483914473311936806710766988517317, 1]
348 floor [11, 1; 43, 1; 641, 1; 245107, 1; 2788433, 1; 1710077340336214906123351716243159844934214935313021315846631640982868666022578551446287, 1]
349 floor [227, 1; 7978375483301031510397, 1; 139471867007183884534443883471819441723, 1; 2805781861196739070889884446657408496421239, 1]
350 ceil [23, 1; 37, 1; 83, 1; 3659, 1; 11243, 1; 670088912987432131, 1; 49553090829402099393706524232241, 1; 14691136326645282783791165328744366719533357, 1]
351 floor [3, 2; 7, 1; 6359, 1; 35021061263507671257391696156759, 1; 202060843096725994022172701597946138797390633286383859709482846478691, 1]
352 floor [11, 1; 89, 1; 419, 1; 9697, 1; 511270822806024077, 1; 3025728472215213071, 1; 4093234049047854941, 1; 225107095215261032814563461840665656736133, 1]
353 ?
354 floor [571018986709, 1; 39717351074494245043762586921800387692118376188139242410200815307557828092853334444916825572921, 1]
355 ceil [79, 1; 24953, 1; 848367011, 1; 17432350267, 1; 510992357493547, 1; 3044786474350216847983988649177119829415258840725908752765264835303, 1]
356 floor [3, 1; 7, 2; 617, 1; 797579394825793, 1; 1621712801171213168393553136941974879303, 1; 773286532960952325655472706217455395632421804617, 1]
357 floor [5, 1; 11, 1; 134152751, 1; 61270474081, 1; 22886833991100529, 1; 17535638310775992653237692520541752670784538987162810932577646682714547, 1]
358 ceil [3, 1; 17, 1; 233, 1; 412937219, 1; 26644687747, 1; 2775428519532822367827413397193850980478599356404018685871631683022123949007508707549, 1]
359 floor [83, 1; 107, 1; 433, 1; 22823069, 1; 142402634738930446415964685733, 1; 3381065930182911983207565419957, 1; 17174548519072311885602474155573513, 1]
360 floor [47, 1; 313, 1; 3557, 1; 42645471853, 1; 650446848878385426680602075677758009683969258474999056570707716420447141855857317151974333, 1]
361 floor [271, 1; 823, 1; 8600341, 1; 41160607, 1; 18498931603, 1; 1987593554857950291835906912602885601488427840278492885179419627023862458025919, 1]
362 ?
363 floor [43, 1; 2513033, 1; 1710116276218317137, 1; 62835995244123152386426917832871749951378089297409106563298098111463363301007946597, 1]
364 floor [239, 1; 1511, 1; 105853385041, 1; 1858744698077, 1; 326846563203147547309101646892772751311671954384471035580926094375459391997827811, 1]
365 ceil [19, 1; 50647, 1; 1213125201611, 1; 2480522284036327, 1; 18213519240817509331, 1; 20171527567811744930841017, 1; 43658824237382446853678793903101, 1]
366 ceil [3, 1; 11, 1; 31, 1; 251, 1; 361777386919825305119311577630473868033832111667641971776757079688259794285068464352111970333028313050521, 1]
367 ceil [5, 1; 23, 2; 83, 1; 509, 1; 155287597, 1; 15781306908119, 1; 1839490401381659433151, 1; 368826362944583330567817791790526047192235141064286489688727, 1]
368 floor [3, 2; 29, 1; 41, 1; 317, 1; 25999, 1; 1457119860437, 1; 133445422028687, 1; 21612900757114217274875983669, 1; 1002532539187322305630367279331341291484222433, 1]
369 floor [229, 1; 5527, 1; 1687718447771, 1; 347901110743718498599187973667395671308529552317674249484122566904601140741173782756475550563, 1]
370 ?
371 ceil [1009, 1; 380430555834389, 1; 7744157785567262193733469665892867177846888890049730844614429226772537928501151473433447824937, 1]
372 ?
373 ceil [5, 1; 37, 1; 103, 1; 193, 1; 6053, 1; 782659, 1; 10178310973, 1; 12202138817860064921694620104141, 1; 5495149923716822096002614617535000420853817108401290233, 1]
374 ceil [3, 1; 3467, 1; 12637, 1; 8577821471496207012319, 1; 1426450496388361149402743591, 1; 14786927673016465226621378178925010707455720876068724893, 1]
375 floor [11, 1; 24533, 1; 786137689453, 1; 13107132931938763, 1; 291087426115648073, 1; 1829974528909997024411188243, 1; 32110167932290900145406169097621899, 1]
376 ?
377 ceil [3, 4; 7, 1; 13, 1; 29, 1; 431, 1; 27421249, 1; 27028999967, 1; 11681761529311, 1; 143182597037783851519226618543, 1; 1665724846827203384515939920740348809198249819, 1]
378 floor [18894847, 1; 2220672120948124519839211, 1; 352720799503241188580639747579, 1; 25709393446641376406109376893686034082521796989818719, 1]
379 floor [5, 1; 152198619089410954152183384838815197620881281530651331819984069628384923087601475251543813256515877317708068835127, 1]
380 ?
381 floor [1181, 1; 25769666671620917693, 1; 100018885073162415029427904484851943330362711260901823707820583824104275791546121623963799671, 1]
382 floor [79, 1; 34663241297, 1; 2223179052521989152922487081691361410529281913695286254307520710052428798281621424730693981917625098849, 1]
383 floor [5, 2; 352190767, 1; 1382874358787818686021904803325547237832103931611825195360527503013251207350148167867615343876549743328921, 1]
384 ?
385 ceil [43, 1; 2974691, 1; 7013659, 1; 54288235768047918074103992378751118123965564161149237042612297040866214429888347743166679459811429709, 1]
386 ceil [3, 1; 5, 1; 17, 1; 73, 1; 107, 1; 35413569327358471, 1; 720660738462814830617, 1; 1916210890136620517289374632360475922054954060794919575613023622057322703, 1]
387 ceil [7, 1; 367, 1; 46507, 1; 85909, 1; 8171231, 1; 172974556575449, 1; 96259301663665301824525548357733, 1; 139504162845842903712696449871823860171063018319661, 1]
388 ceil [3, 1; 5147, 1; 15689160440728927, 1; 1608331434372434218311970236937336007516337915015098013704901028940588066246332329324402076952831, 1]
389 ceil [5141847406039992227, 1; 151551936143109102959375960649310656851935730559210823027754324672377885022749373336866899385143979, 1]
390 ceil [3, 2; 5, 1; 7, 1; 11, 1; 19, 1; 251, 1; 104292193, 1; 4213397491, 1; 214632693319589130346591387803522924671940525640530717475066778706929210156928407527123398883, 1]
391 ceil [3089, 1; 28221097, 1; 7189124113, 1; 6214616337845536037, 1; 800310584726622401491166682238327834838693889394149608936341349262285472392773, 1]
392 floor [3, 1; 313884302637102642787, 1; 30973388432677533211931, 1; 213742600612652862657408047362384480134559557845704828855166635341701406427, 1]
393 ?
394 ?
395 ceil [19, 1; 53161, 1; 79559, 1; 411586061, 1; 59790615448086569, 1; 68329699902280978815971232407, 1; 369080748891073514180149306592570615356162714694592587, 1]
396 ceil [3, 1; 48953, 1; 2759027, 1; 16833225139427, 1; 14624020711664965070076378968593933772343340352507820102900562663192358124138750549478185210211, 1]
397 floor [83, 1; 1760349297527, 1; 10179520075480423695943, 1; 134127055770930792981678719217293939749634643893459646612273347868142958596760937707, 1]
398 ceil [23, 1; 176796733, 1; 217238645652478766996481059, 1; 1603648391823747862380073290180384352427, 1; 281645179751233383202666124172086949270888409, 1]
399 ceil [3, 2; 5, 1; 7, 2; 509, 1; 710974874972928024186323478701938729448223187443630304917256350741765451405337950956982057786439965315001429983037, 1]
400 ceil [13, 1; 26573, 1; 38153, 1; 723619264028356427659, 1; 167335418010543893378506379275236817655942554451299791344067339816250312394491938907367723, 1]
401 ceil [3, 1; 1063945461401987871073865632938303231070088071081895006096477438631022327410032030089085370195095950495287039912415549019, 1]
402 floor [7, 1; 19, 1; 97, 1; 4673, 1; 102749604746773747423710979642087, 1; 1030555298426081827795721660482442350248352219938071086460243896044396838704510763, 1]
403 floor [37, 1; 345063392887131201429361826898909156022731266296830812788046736853304538619469847596460120063274362322795796728350988871, 1]
404 ceil [5, 1; 31, 1; 73, 1; 4441, 1; 18311, 1; 98076568087, 1; 1857817188785166107143, 1; 152305286060320150884100414312571916316917969066544867915721573408647369806227, 1]
405 ?
406 ?
407 floor [3, 1; 1543, 1; 69444202593217937, 1; 6447357755286017837080177587253, 1; 98563393915774324470940922492102529601241333561202985674017078343580831, 1]
408 floor [72845116691, 1; 131089567559, 1; 188487524638037, 1; 174055500099269156048463925411271, 1; 1304102279750407824681784355936030541660050556304013233, 1]
409 ceil [3, 3; 19, 1; 53, 1; 26293, 1; 75017, 1; 1237297, 1; 12314408551375255999454509997585088681446259095786813151701234852692452135374145420580609524839168719183, 1]
410 ceil [7, 1; 11, 1; 8501634164843, 1; 1849067334566700779, 1; 2077314121700919282227810047, 1; 649923954213007497550982426051177641215204101181595966384782919, 1]
411 ceil [3, 1; 859, 1; 2879, 1; 1051845758012022933094451, 1; 418824843026847965752407677691488014030832138081158568204275727764072850339767452357694141901, 1]
412 ?
413 floor [3, 1; 7, 1; 31, 1; 37, 1; 173, 1; 66713, 1; 6538898649471342086806151, 1; 7192115884270940994730383194169851842355143422550524584589702845783128885251422185618733, 1]
414 ?