_____________________________________________________________________Investigating The Iterative Formula:x = kx(1 - x)by Adi Cox 11/8/14_____________________________________________________________________where k = 4 and the starting value of x = 0.2 we get chaotic fractions:x0 = (4/5)(4/5) = 16/25 = (2^4)/(5^2) = 0.64x1 = (64/25)(9/25) = 576/625 = (2^6*3^2)/(5^4) = ((2^6)*3^2)/(5^4) = 0.9216x2 = (2304/625)(49/625) = 112896/390625 = (2^8*3^2*7^2)/(5^8) = ((2^8)*(3*7)^2)/(5^8) = 0.28901376x3 = (451584/390625)(277729/390625) = 125417972736/152587890625 = (2^10*3^2*7^2*17^2*31^2)/(5^16) = ((2^10)*(3*7*17*31)^2)/(5^16) = 0.8219392261226496x4 = (501671890944/152587890625)(27169917889/152587890625) = 13630384084167842697216/23283064365386962890625 = (2^12*3^2*7^2*17^2*31^2*191^2*863^2)/(5^32) = ((2^12)*(3*7*17*31*191*863)^2)/(5^32) = 0.58542053873419795759415150247936 xn = [2^(2+2n)*MnValuesSquared]/[5^(2^n)]How do we find the M values?nth M value {1, 2, 3, 4 }nth prime {2, 4, 7,11, 43,150 }primes {3, 7, 17*31, 191*863 }M values {3, 7, 527, 164833 }Below are the list of M valuesM0 ---> 0M1 ---> 3M2 ---> 7M3 ---> 527M4 ---> 164833M5 ---> ?_____________________________________________________________________The chaotic fraction for x5xn = [2^(2+2n)*MnValuesSquared]/[5^(2^n)]x5 = [2^(2+2*6)*(*M1*M2*M3*M4*M5)^2]/[5^(2^6)] = [2^(2+2*6)*(3*7*527*164833*M5)^2]/[5^(2^6)] = [73786976294838206464*(1824206811*M5)^2]/[5^64] = 0.970813326249439M5 = {([0.970813326249439*5^(2^n)]/[2^(2+2*6)])^(1/2)}/{M1*M2*M3*M4}_____________________________________________________________________The html file below gives the output for the first 1000 values for the iterative formula x = kx(1 - x) where k = 4 and the starting value of x = 0.2For some reason the answers are slightly wrong. The first answer should be 0.6400000000000000 but we get:1 x = 0.6400000000000001_____________________________________________________________________

_____________________________________________________________________x = kx(1 - x)The starting value of x = 0.2k = 41 x = 0.64000000000000012 x = 0.92159999999999993 x = 0.289013760000000454 x = 0.82193922612265045 x = 0.5854205387341966 x = 0.9708133262494397 x = 0.113339247303757458 x = 0.401973849297500639 x = 0.961563495113803510 x = 0.1478365599133197311 x = 0.503923645865260612 x = 0.999938420012496113 x = 0.0002463047816361171414 x = 0.000984976462362641315 x = 0.00393602513492493216 x = 0.01568213136424868217 x = 0.0617448084804925218 x = 0.2317295484247992619 x = 0.712123859246551520 x = 0.820013873353396821 x = 0.590364483445424422 x = 0.967337040526566523 x = 0.1263843622074811724 x = 0.4416454207875575325 x = 0.986378972339755126 x = 0.0537419810628948427 x = 0.2034151221373211928 x = 0.648149640892719529 x = 0.91220673561343330 x = 0.320342428459669331 x = 0.870892627952923932 x = 0.4497546341206959433 x = 0.989901612830619534 x = 0.0399856389838311535 x = 0.153547150635543536 x = 0.519881692668996937 x = 0.998418873186462338 x = 0.0063145074061489539 x = 0.0250985376094665640 x = 0.0978744040773310141 x = 0.3531800204153533542 x = 0.913775574379055843 x = 0.3151590961891299644 x = 0.863335361113522745 x = 0.471949661458024246 x = 0.996852714030722247 x = 0.01254952224122164648 x = 0.04956812693095491449 x = 0.1884445108940466250 x = 0.611732708831800651 x = 0.950063207108432352 x = 0.1897724384290895653 x = 0.615035440167067954 x = 0.947067390022275855 x = 0.2005229951146813356 x = 0.641254094179675357 x = 0.920189123509917758 x = 0.2937644019358686759 x = 0.829867512364520260 x = 0.564749697145772561 x = 0.98322990687812362 x = 0.0659554283942424863 x = 0.2464212394382977564 x = 0.742791248767963565 x = 0.764209638086771366 x = 0.720773068568229267 x = 0.805037008779871868 x = 0.627809693098513569 x = 0.934658729400255270 x = 0.2442871558246229671 x = 0.738443765294957472 x = 0.772578283167853273 x = 0.702804318181062774 x = 0.835481634108457175 x = 0.549808292703677376 x = 0.990076535911779277 x = 0.039299955794842278 x = 0.1510218770774625679 x = 0.512857078885849480 x = 0.999338782090092281 x = 0.002643122803133698482 x = 0.01054454681992501283 x = 0.04173343740914968584 x = 0.1599670304446650685 x = 0.537510318461522686 x = 0.994371904035660787 x = 0.0223856820006220788 x = 0.0875382529679563889 x = 0.3195012289410978490 x = 0.86968077458490491 x = 0.453344499609221692 x = 0.991293057133144493 x = 0.0345245280510755894 x = 0.1333303400557043295 x = 0.4622134419053382596 x = 0.994288704109434997 x = 0.02271470795926194598 x = 0.0887950000063495699 x = 0.32364179192088777100 x = 0.8755911297724981101 x = 0.435725212944874102 x = 0.9834750069960728103 x = 0.06500767044058935104 x = 0.2431266928979083105 x = 0.736064416393738106 x = 0.7770943652507356107 x = 0.6928748509851677108 x = 0.8511971674297975109 x = 0.5066421983571473110 x = 0.9998235248039372111 x = 0.000705776210271844112 x = 0.002821112360851433113 x = 0.011252614743595537114 x = 0.04450397362011101115 x = 0.1700934798085259116 x = 0.56464675174061117 x = 0.9832831899575518118 x = 0.06574943321781154119 x = 0.24570578099739232120 x = 0.7413378007274152121 x = 0.7670242637602178122 x = 0.7147921702532545123 x = 0.8154572943915878124 x = 0.6019467816605565125 x = 0.9584274148362193126 x = 0.15937722130632362127 x = 0.5359044905399951128 x = 0.9948434702362536129 x = 0.02051975985816785130 x = 0.08039479725412389131 x = 0.2957258953143688132 x = 0.8330883606195351133 x = 0.5562085760791623134 x = 0.9873623839006122135 x = 0.04991162703484937136 x = 0.18968182608633385137 x = 0.6148105237555506138 x = 0.9472741745399046139 x = 0.19978325115858786140 x = 0.6394796148603699141 x = 0.9221817481536115142 x = 0.2870502861038421143 x = 0.818609677406178144 x = 0.5939514938525249145 x = 0.9646924672115159146 x = 0.13624364366749683147 x = 0.4707252529108039148 x = 0.9965719567314544149 x = 0.013665167151578403150 x = 0.05391372143319131151 x = 0.20402812829766223152 x = 0.6496026046440596153 x = 0.9104762427348527154 x = 0.32603701660111306155 x = 0.8789475216278343156 x = 0.4255951034084882157 x = 0.9778556454528259158 x = 0.08661592843545267159 x = 0.31645443750686886160 x = 0.8652441059563204161 x = 0.4663869722566728162 x = 0.9954806574637053163 x = 0.0179956723173374164 x = 0.07068731238073767165 x = 0.2627624649965027166 x = 0.7748734079418576167 x = 0.6977784384257166168 x = 0.84353475717554169 x = 0.5279354824493709170 x = 0.9968784352812835171 x = 0.012447282209693444172 x = 0.04916938950114277173 x = 0.1870070425489107174 x = 0.6081416343440824175 x = 0.9532215476855631176 x = 0.17836091485401137177 x = 0.5861931956258059178 x = 0.9702829321112463179 x = 0.1153358550593957180 x = 0.40813398238845505181 x = 0.9662425392327811182 x = 0.13047157843907417183 x = 0.45379498263476276184 x = 0.9914603854811126185 x = 0.03386675801102485186 x = 0.13087920285139013187 x = 0.45499934844949924188 x = 0.9918997654401217189 x = 0.03213848303981299190 x = 0.12442240379085057191 x = 0.4357658769030284192 x = 0.9834959097198525193 x = 0.06492682113668913194 x = 0.24284531613509402195 x = 0.735485874265361196 x = 0.7781856120859143197 x = 0.6904510609135408198 x = 0.8549135735876271199 x = 0.49614542113304200 x = 0.9999405688870334201 x = 0.00023771032363756306202 x = 0.0009506152697583969203 x = 0.0037988464014691962204 x = 0.015137660669948963205 x = 0.05963404759756177206 x = 0.22431131185877404207 x = 0.6959829889238794208 x = 0.8463626722098502209 x = 0.5201315971986076210 x = 0.998378875176932211 x = 0.006473987109504037212 x = 0.02572829840164005213 x = 0.10026541225198488214 x = 0.3608490374316976215 x = 0.9225480384652597216 x = 0.2858126207566457217 x = 0.8164950662914541218 x = 0.5993234920526723219 x = 0.9605393757058509220 x = 0.15161393369786041221 x = 0.5145085952260848222 x = 0.9991580026582625223 x = 0.0033651535288560692224 x = 0.013415317082333188225 x = 0.05294138539965459226 x = 0.20055438044647933227 x = 0.6413292837208326228 x = 0.9201041342518256229 x = 0.29405006553809643230 x = 0.8303384979805505231 x = 0.5635059070078153232 x = 0.9838679991004589233 x = 0.06348703778607338234 x = 0.2378257352768923235 x = 0.7250586196675913236 x = 0.7973944708532739237 x = 0.6462261148236049238 x = 0.9144716933743756239 x = 0.31285286156551023240 x = 0.8599037943031278241 x = 0.4818770353848475242 x = 0.9986862326142317243 x = 0.005248165604097454244 x = 0.02088248944755769245 x = 0.08178564432812133246 x = 0.30038701083982144247 x = 0.8406186182341537248 x = 0.5359158276490233249 x = 0.9948402132971426250 x = 0.020532653216153815251 x = 0.08044425347223594252 x = 0.29589190222212236253 x = 0.8333595376859854254 x = 0.5554856745351444255 x = 0.9876853596855201256 x = 0.048651959793619665257 x = 0.18513978640743872258 x = 0.6034521835857868259 x = 0.9571905828453307260 x = 0.1639070838301874261 x = 0.5481662068018853262 x = 0.9907200660892721263 x = 0.03677526694936169264 x = 0.14169138676065948265 x = 0.48645975071400277266 x = 0.9992666465970923267 x = 0.002931262382776572268 x = 0.011690680334479566269 x = 0.04621603331118631270 x = 0.1763204463046625271 x = 0.5809261860783486272 x = 0.97380380962725273 x = 0.10203979993081858274 x = 0.36651071664358836275 x = 0.9287224449159666276 x = 0.2647882609011041277 x = 0.7787017511602916278 x = 0.6893013356007476279 x = 0.8566600173590926280 x = 0.4911745280696471281 x = 0.9996884441808263282 x = 0.001245835008581147283 x = 0.004977131614850162284 x = 0.019809439102954487285 x = 0.07766810090152329286 x = 0.28654306801549634287 x = 0.817744552751052288 x = 0.5961535967881358289 x = 0.9630179432988184290 x = 0.14245753673332875291 x = 0.4886535478448042292 x = 0.9994850320939594293 x = 0.0020588108563852057294 x = 0.008218288616971344295 x = 0.032602993396718016296 x = 0.12616015287316631297 x = 0.4409750748007425298 x = 0.9860642328208882299 x = 0.05496624628896565300 x = 0.2077798322314657301 x = 0.6584294941973187302 x = 0.899600381473527303 x = 0.36127814050484663304 x = 0.9230249827928277305 x = 0.28419945573251115306 x = 0.8137205003754223307 x = 0.6063177905767786308 x = 0.954786109627489309 x = 0.17267837795957422310 x = 0.5714422229792986311 x = 0.9795840351031048312 x = 0.0799966130968959313 x = 0.2943886199596858314 x = 0.83089584159167315 x = 0.5620317680693618316 x = 0.9846082390007556317 x = 0.060619418770346316318 x = 0.22777881935316682319 x = 0.7035825152289769320 x = 0.8342166379721736321 x = 0.5531969556103082322 x = 0.9886803356551795323 x = 0.04476611817576423324 x = 0.17104845135695096325 x = 0.5671635145813589326 x = 0.9819562492363183327 x = 0.07087269528823933328 x = 0.26339902540327886329 x = 0.7760799152795269330 x = 0.695119521516997331 x = 0.8477134892919126332 x = 0.5163813174577719333 x = 0.9989266097533908334 x = 0.004288952319950899335 x = 0.017082228831792348336 x = 0.06716170515972253337 x = 0.25060404207904413338 x = 0.7512066246907553339 x = 0.747580926845912340 x = 0.7548147386484766341 x = 0.7402777958700343342 x = 0.7690663232473526343 x = 0.7104132547766047344 x = 0.8229050488572626345 x = 0.5829293176899555346 x = 0.9724909130699138347 x = 0.10700934826543682348 x = 0.3822333905969731349 x = 0.9445241028388597350 x = 0.20959328798122762351 x = 0.6626557664577831352 x = 0.8941724065521245353 x = 0.3785124556516268354 x = 0.9409631062728081355 x = 0.22220615562494458356 x = 0.6913223201093099357 x = 0.853583079311963358 x = 0.4999160240970804359 x = 0.999999971792191360 x = 1.1283123272727172e-7361 x = 4.5132487998553857e-7362 x = 0.000001805298705165565363 x = 0.0000072211817842486364 x = 0.000028884518555128958365 x = 0.00011553473695886719366 x = 0.00046208555473369213367 x = 0.0018474881266951943368 x = 0.007376299657267658369 x = 0.029287559442535405370 x = 0.11371919321774145371 x = 0.4031485532465897372 x = 0.9624791890470853373 x = 0.14445199879340137374 x = 0.4943424753519701375 x = 0.9998719696594278376 x = 0.0005120557952163029377 x = 0.0020471743763155535378 x = 0.008171933813554043379 x = 0.03242061324520374380 x = 0.12547806832803465381 x = 0.4389332907867989382 x = 0.9850834281034814383 x = 0.05877627111749847384 x = 0.22128648428408312385 x = 0.6892751046290934386 x = 0.856699739070583387 x = 0.49106118458791187388 x = 0.9996803903161146389 x = 0.0012780301341416536390 x = 0.005105587092471518391 x = 0.020318080291650824392 x = 0.07962102361965141393 x = 0.2931260648696413394 x = 0.8288126998547206395 x = 0.5675288336569977396 x = 0.9817594264997022397 x = 0.0716314199147123398 x = 0.2660014383828578399 x = 0.7809786926444341400 x = 0.6842038971192985401 x = 0.8642756971442516402 x = 0.46921286588027805403 x = 0.9962086094907769404 x = 0.015108063468918525405 x = 0.059519239548550616406 x = 0.22390679868845145407 x = 0.695090176758163408 x = 0.8477592917298749409 x = 0.5162539000621432410 x = 0.9989432429310794411 x = 0.004222561333671588412 x = 0.01681892523781988413 x = 0.06614419596665802414 x = 0.24707656522632945415 x = 0.7441189445691553416 x = 0.7616237636097668417 x = 0.7262120252586435418 x = 0.7953124785135314419 x = 0.6511621601367803420 x = 0.9086000053711295421 x = 0.33218414244285177422 x = 0.8873513518094357423 x = 0.3998357210056111424 x = 0.9598684688541368425 x = 0.15408396541500727426 x = 0.5213683880679765427 x = 0.9981735679655055428 x = 0.007292384722071518429 x = 0.028956823388547263430 x = 0.11247330307116699431 x = 0.39929223666971364432 x = 0.9594317856200442433 x = 0.15568973744791112434 x = 0.5258017724052465435 x = 0.9973370741629914436 x = 0.010623338651980594437 x = 0.04204193331146371438 x = 0.16109763661959262439 x = 0.5405807523806972440 x = 0.9934128101448662441 x = 0.02617519513978507442 x = 0.10196021719671697443 x = 0.36625732522366106444 x = 0.9284515877746817445 x = 0.2657169477334168446 x = 0.7804458056826138447 x = 0.6854006003001185448 x = 0.8625064696334228449 x = 0.47435623789564924450 x = 0.9973695898605419451 x = 0.010493964327825279452 x = 0.04153536416204644453 x = 0.1592407107438905454 x = 0.5355324271426845455 x = 0.9949497864853993456 x = 0.02009883543223044457 x = 0.07877948898599424458 x = 0.2902931244043994459 x = 0.8240921053117253460 x = 0.5798572290984543461 x = 0.974491291842868462 x = 0.09943205586114515463 x = 0.358181288513485464 x = 0.9195498122892186465 x = 0.2959118200323257466 x = 0.8333920591899288467 x = 0.5553989394763962468 x = 0.9877238300195623469 x = 0.04850186252419632470 x = 0.18459772742352112471 x = 0.6020856258143701472 x = 0.9583141000083537473 x = 0.159792742934131474 x = 0.5370360889588709475 x = 0.9945133124585224476 x = 0.021826335205199297477 x = 0.0853997851868383478 x = 0.3124266475075207479 x = 0.8592649497389284480 x = 0.48371478355634095481 x = 0.9989391669015328482 x = 0.004238830926417435483 x = 0.016883452955178728484 x = 0.06639360788595598485 x = 0.24794198687136765486 x = 0.7458670320705848487 x = 0.7581976101632081488 x = 0.7333359764240321489 x = 0.7822172884249741490 x = 0.68141360845622491 x = 0.8683564106675732492 x = 0.4572542188804087493 x = 0.9926911927859039494 x = 0.029021554204813116495 x = 0.11271721438540085496 x = 0.40004817586638575497 x = 0.9600385314094522498 x = 0.15345819847453795499 x = 0.519635119181949500 x = 0.9984578483788427501 x = 0.006159093558138804502 x = 0.02448463649872359503 x = 0.09554055629699586504 x = 0.3456502335978257505 x = 0.9047045984463769506 x = 0.3448567519854275507 x = 0.9037222903819553508 x = 0.3480332489949927509 x = 0.9076244263559285510 x = 0.3353693081520007511 x = 0.8915869412065964512 x = 0.3866386699058464513 x = 0.9485968353571373514 x = 0.19504351723024563515 x = 0.6280061744668021516 x = 0.9344576771934985517 x = 0.24498610691051947518 x = 0.739871657325388519 x = 0.7698463520478867520 x = 0.708731785145792521 x = 0.8257241674794036522 x = 0.5756150668793978523 x = 0.9771294466432968524 x = 0.0893899645834455525 x = 0.32559759526086346526 x = 0.8783352048848256527 x = 0.427449890979028528 x = 0.9789459267241802529 x = 0.08244319709726469530 x = 0.30258526539858505531 x = 0.8441096902490116532 x = 0.5263540843069171533 x = 0.9972218489613757534 x = 0.011081731661723692535 x = 0.04383570754040497536 x = 0.1676565531393482537 x = 0.5581913333151245538 x = 0.9864550749080323539 x = 0.053445840384882724540 x = 0.20235753012174545541 x = 0.6456358404990893542 x = 0.9151608078484953543 x = 0.3105660145063391544 x = 0.8564590605599498545 x = 0.49174775257887215546 x = 0.999727601650002547 x = 0.0010892965965478237548 x = 0.004352440117890292549 x = 0.017333985531641886550 x = 0.06813407390892287551 x = 0.25396728752598524552 x = 0.7578716175707151553 x = 0.7340089154058514554 x = 0.7809593100423082555 x = 0.6842474644022005556 x = 0.8642114874454394557 x = 0.46939996965112213558 x = 0.9962545525705909559 x = 0.014925676211850439560 x = 0.05881160160587776561 x = 0.22141118848971714562 x = 0.6895530964051523563 x = 0.8562784945728762564 x = 0.4922625372195401565 x = 0.9997605266788839566 x = 0.0009576638945781675567 x = 0.0038269870977727556568 x = 0.015249365070104947569 x = 0.06006728774025444570 x = 0.2258368347351357571 x = 0.6993382352478028572 x = 0.8410570718731665573 x = 0.534720294901207574 x = 0.9951780044878928575 x = 0.019194975485553507576 x = 0.07530611360665003577 x = 0.2785404114404494578 x = 0.8038226025401383579 x = 0.6307673047429487580 x = 0.9315996480410591581 x = 0.25488697524333565582 x = 0.7596784203785555583 x = 0.7302684719587929584 x = 0.7879057232870506585 x = 0.6684411779942411586 x = 0.8865102782236496587 x = 0.40243921930990795588 x = 0.9619275762845589589 x = 0.14649165707149192590 x = 0.5001274059197613591 x = 0.9999999350709264592 x = 2.597162773854525e-7593 x = 0.000001038864839731631594 x = 0.000004155455041965903595 x = 0.00001662175109663719596 x = 0.00006648589925611068597 x = 0.00026592591552524315598 x = 0.001063420795730781599 x = 0.004249159727767953600 x = 0.01692441747750347601 x = 0.06655192628220258602 x = 0.2484910695613234603 x = 0.7469730316383718604 x = 0.7560172865734072605 x = 0.7378205959023596606 x = 0.7737654566585863607 x = 0.7002098989620628608 x = 0.8396639854304024609 x = 0.5385135080061414610 x = 0.9940668388042435611 x = 0.023591835175926626612 x = 0.09214104195583414613 x = 0.3346042813725094614 x = 0.8905770250387839615 x = 0.38979835004741276616 x = 0.9514223853909098617 x = 0.18487131987192348618 x = 0.6027756598429457619 x = 0.9577486549753885620 x = 0.16186467547289085621 x = 0.5426580092277863622 x = 0.9927211769948884623 x = 0.028903366963087523624 x = 0.1122718493651385625 x = 0.3986675248210806626 x = 0.9589269178964547627 x = 0.157544336120243628 x = 0.5308964731066995629 x = 0.996181631798268630 x = 0.015215153064031931631 x = 0.05993460872508004632 x = 0.22536980560820638633 x = 0.6983130253133025634 x = 0.8426877759643417635 x = 0.5302603528184525636 x = 0.9963372441892111637 x = 0.014597360122637721638 x = 0.05753710880035099639 x = 0.21690635964499025640 x = 0.6794319631621936641 x = 0.8712166823830448642 x = 0.44879269888210244643 x = 0.9895112492488838644 x = 0.0415149474351887645 x = 0.15916582629856887646 x = 0.5353282641490507647 x = 0.9950076550088596648 x = 0.019869685930519458649 x = 0.0778995260461679650 x = 0.28732475955180126651 x = 0.8190769684012034652 x = 0.5927595529435898653 x = 0.9655826613508214654 x = 0.1329311417979455655 x = 0.46104181335295996656 x = 0.9939290387726977657 x = 0.024136418628315684658 x = 0.09421540769645752659 x = 0.34135545859619126660 x = 0.8993276379311008661 x = 0.3621497503374706662 x = 0.9239892346719132663 x = 0.2809325155293013664 x = 0.8080377489907208665 x = 0.6204509807869187666 x = 0.9419662449098773667 x = 0.21866335344104926668 x = 0.6833987652118562669 x = 0.8654595716750658670 x = 0.4657572058843097671 x = 0.9953097242046017672 x = 0.018673108433445478673 x = 0.07329769381951307674 x = 0.2717005676010159675 x = 0.7915174766652068676 x = 0.6600702431950025677 x = 0.897510068973971678 x = 0.36794298025723526679 x = 0.9302437741466362680 x = 0.2595611792322333681 x = 0.768756693871223682 x = 0.7110793579976389683 x = 0.8217820185092184684 x = 0.5858253302565322685 x = 0.9705360507454287686 x = 0.11438329979558139687 x = 0.4051990420938222688 x = 0.9640511135202844689 x = 0.13862625616233654690 x = 0.47763606905900313691 x = 0.9979994183714653692 x = 0.007986317206728958693 x = 0.031690143776809857694 x = 0.12274351425685989695 x = 0.43071017585894367696 x = 0.980795681082006697 x = 0.07534205221155996698 x = 0.27866250952044214699 x = 0.8040388612328465700 x = 0.6302414834409356701 x = 0.932148623964418702 x = 0.2529902672226402703 x = 0.7559447676530292704 x = 0.7379691036441476705 x = 0.7734828228432038706 x = 0.7008285824388513707 x = 0.8386715219024061708 x = 0.5412064010092322709 x = 0.9932081300634654710 x = 0.026982961757199102711 x = 0.10501952612803453712 x = 0.3759617010395104713 x = 0.9384580015639528714 x = 0.2310183234581792715 x = 0.7105954307390051716 x = 0.8225982582074116717 x = 0.5837214552061767718 x = 0.9719628717526406719 x = 0.10900419074800201720 x = 0.3884891085895008721 x = 0.9502612843873435722 x = 0.1890591031274392723 x = 0.6132630346083501724 x = 0.9486859399652308725 x = 0.19472370911006934726 x = 0.6272255448819458727 x = 0.935254642917968728 x = 0.24221358327340867729 x = 0.7341846534050568730 x = 0.7806301924382137731 x = 0.6849867803683645732 x = 0.863119564355786733 x = 0.4725767279282569734 x = 0.9969918565955166735 x = 0.011996377910965892736 x = 0.04740985931193273737 x = 0.1806486582078219738 x = 0.5920588819821417739 x = 0.9661006489927924740 x = 0.1310007400339911741 x = 0.4553581845781511742 x = 0.9920284332633662743 x = 0.03163208344158876744 x = 0.1225259789549325745 x = 0.4300534537442718746 x = 0.9804299226675812747 x = 0.0767483576224877748 x = 0.2834321888989538749 x = 0.8123935327796064750 x = 0.609641122709908751 x = 0.9519152968436436752 x = 0.18309025791488587753 x = 0.5982728614861857754 x = 0.9613697787812678755 x = 0.14855170890929592756 x = 0.5059363947576949757 x = 0.9998590368691233758 x = 0.000563773041089925759 x = 0.002253820804192261760 x = 0.008994964383899405761 x = 0.035656219998527146762 x = 0.13753941589577512763 x = 0.47448929988329647764 x = 0.9973968167182224765 x = 0.010385626874316115766 x = 0.04111106251497439767 x = 0.15768377221545704768 x = 0.5312784007814436769 x = 0.9960866465782215770 x = 0.015592156347098835771 x = 0.06139616403018584772 x = 0.2305067002902574773 x = 0.7094934456462194774 x = 0.824449984925098775 x = 0.5789288291284147776 x = 0.97508095972967777 x = 0.09719232680934263778 x = 0.35098391367491427779 x = 0.9111768240654184780 x = 0.3237344774059037781 x = 0.8757218621785207782 x = 0.4353323291244189783 x = 0.9832723693741101784 x = 0.06579126799813471785 x = 0.2458511082133293786 x = 0.7416333632144286787 x = 0.766453271126736788 x = 0.7160106172234485789 x = 0.8133576529869793790 x = 0.6072279252579675791 x = 0.9540086881794869792 x = 0.17550444423016565793 x = 0.5788105371425053794 x = 0.9751555969412392795 x = 0.09690863478165851796 x = 0.35006940514565454797 x = 0.9100832669064884798 x = 0.32732685681320706799 x = 0.8807359424879732800 x = 0.4201605683911792801 x = 0.9745026606415217802 x = 0.0993889001764676803 x = 0.35804298679271906804 x = 0.9193928256050715805 x = 0.2964386313239763806 x = 0.8342510767309759807 x = 0.5531048708167331808 x = 0.9887194907821524809 x = 0.044613037318534714810 x = 0.17049085687899898811 x = 0.5656948983986546812 x = 0.9827367212975618813 x = 0.0678610316435204814 x = 0.2530236481111901815 x = 0.756010726430779816 x = 0.7378340318095392817 x = 0.7737398932528764818 x = 0.7002658833676153819 x = 0.8395743038359548820 x = 0.5387571686973067821 x = 0.993991527498274822 x = 0.023889483039687937823 x = 0.0932751025591376824 x = 0.33829943120687983825 x = 0.8954117042079256826 x = 0.3745983367015358827 x = 0.9370976913679145828 x = 0.2357824328033573829 x = 0.7207563087387504830 x = 0.805066608608166831 x = 0.6277374572492481832 x = 0.934732568061986833 x = 0.24403037706492278834 x = 0.7379182085378976835 x = 0.7735797041844699836 x = 0.7006165818333518837 x = 0.8390119483740082838 x = 0.5402835954386352839 x = 0.9935089277541455840 x = 0.025795752907814568841 x = 0.10052132815893418842 x = 0.3616671629763922843 x = 0.9234561048039999844 x = 0.2827397092168955845 x = 0.8111918641953635846 x = 0.6126384946344577847 x = 0.949250278105933848 x = 0.19269675048696747849 x = 0.6222588513549235850 x = 0.9402110930614989851 x = 0.22485677418240158852 x = 0.6971848211467442853 x = 0.8444725852373061854 x = 0.5253545520797076855 x = 0.9974285867553496856 x = 0.010259204314302458857 x = 0.04061581216455942858 x = 0.1558646718670906859 x = 0.5262835037234191860 x = 0.9972367097280841861 x = 0.011022617995156171862 x = 0.04360447955075612863 x = 0.16681251565545527864 x = 0.5559444011046151865 x = 0.9874808959401837866 x = 0.049449504373423034867 x = 0.1880170035625834868 x = 0.6106664397357237869 x = 0.9510117564648778870 x = 0.18635358212186307871 x = 0.6065036982088524872 x = 0.9546278490713508873 x = 0.17325407539502835874 x = 0.5729484030161688875 x = 0.9787141219895624876 x = 0.08333115763104938877 x = 0.30554830319567433878 x = 0.8487541504396745879 x = 0.5134821702044036880 x = 0.999272924346318881 x = 0.002906188058703367882 x = 0.011590968518683268883 x = 0.04582647186992865884 x = 0.17490562538353316885 x = 0.5772545903709133886 x = 0.9761269130664896887 x = 0.09321265061510191888 x = 0.33809620952163544889 x = 0.8951486505149513890 x = 0.3754301759848515891 x = 0.9379294357793397892 x = 0.23287123711195662893 x = 0.714568896151614894 x = 0.8158407552171115895 x = 0.6009784693755386896 x = 0.9592133948902937897 x = 0.15649223181332483898 x = 0.5280096527816377899 x = 0.9968618374042084900 x = 0.01251325812525583901 x = 0.04942670598538619902 x = 0.1879348268832815903 x = 0.6104613109105301904 x = 0.9511931951677088905 x = 0.18569880253741522906 x = 0.6048590290943412907 x = 0.9560183360695684908 x = 0.1681891086733686909 x = 0.5596061295881056910 x = 0.9857884372621039911 x = 0.056038376889771944912 x = 0.21159230882132726913 x = 0.6672840146759493914 x = 0.8880642337355871915 x = 0.3976246019808466916 x = 0.9580771115216797917 x = 0.16066143959981835918 x = 0.539397365702129919 x = 0.9937913903029308920 x = 0.02468025145079446921 x = 0.09628454655648008922 x = 0.3480553306035724923 x = 0.9076512697680413924 x = 0.33528176902601436925 x = 0.8914716175392029926 x = 0.3869998906449602927 x = 0.9489239011429962928 x = 0.19386932393021356929 x = 0.6251360366762219930 x = 0.937363889299869931 x = 0.23485131334596765932 x = 0.7187846958625671933 x = 0.8085330274252961934 x = 0.619229483951126935 x = 0.9431373206269927936 x = 0.21451726027011936937 x = 0.673998421265285938 x = 0.8788981975887536939 x = 0.4257446234559752940 x = 0.9779445562172203941 x = 0.0862760047292973942 x = 0.3153298229489903943 x = 0.863587702831795944 x = 0.4712159293979934945 x = 0.9966859091183148946 x = 0.01321243073325259947 x = 0.05215144962948637948 x = 0.19772670372411805949 x = 0.6345234174340516950 x = 0.9276138006474556951 x = 0.2685857499833525952 x = 0.7857897795569302953 x = 0.673296807603205954 x = 0.8798728658981511955 x = 0.42278642301730135956 x = 0.9761522541181475957 x = 0.09311612359282818958 x = 0.33778204447949334959 x = 0.8947413396269877960 x = 0.37671709915796475961 x = 0.9392053054398917962 x = 0.22839479869380586963 x = 0.7049224584936871964 x = 0.8320271440196124965 x = 0.5590319025367182966 x = 0.9860609379315816967 x = 0.054979058468284873968 x = 0.20782544639290315969 x = 0.6585361208979748970 x = 0.8994651934824909971 x = 0.3617102367839845972 x = 0.9235037655586334973 x = 0.28257824223063216974 x = 0.8109111169939133975 x = 0.6133371093183887976 x = 0.9486187986054064977 x = 0.19496469415136713978 x = 0.627813848743324979 x = 0.9346544802776747980 x = 0.24430193109817788981 x = 0.7384739902395161982 x = 0.7725206239169727983 x = 0.7029300381596156984 x = 0.8352775984501478985 x = 0.5503557279100058986 x = 0.9898572026666139987 x = 0.04015968398255974988 x = 0.1541875350599227989 x = 0.5216549563682712990 x = 0.998124251458753991 x = 0.007488920434627826992 x = 0.029731346021406563993 x = 0.11538957234064781994 x = 0.40829927574276087995 x = 0.9663639086827913996 x = 0.1300188187124363997 x = 0.4524557019722358998 x = 0.9909581589001887999 x = 0.035840344837348331000 x = 0.13822325807715316