# Factorizations to support known members of OEIS sequence A298398, n = 1..57 # This is a simple summary file giving the factorization of only the sequence value for each n. n=1 ---------- k=3: 5 P_1 = 5 = 2*2 + 1 ---------- a(1) = 3 n=2 ---------- k=3: 41 P_1 = 41 = 10*4 + 1 ---------- a(2) = 3 n=3 ---------- k=5: 7813 P_1 = 13 = 2*6 + 1 P_2 = 601 = 100*6 + 1 ---------- a(3) = 5 n=4 ---------- k=3: 3281 P_1 = 17 = 2*8 + 1 P_2 = 193 = 24*8 + 1 ---------- a(4) = 3 n=5 ---------- k=9: 1743392201 P_1 = 41 = 4*10 + 1 P_2 = 42521761 = 4252176*10 + 1 ---------- a(5) = 9 n=6 ---------- k=5: 122070313 P_1 = 313 = 26*12 + 1 P_2 = 390001 = 32500*12 + 1 ---------- a(6) = 5 n=7 ---------- k=15: 14596463012695313 P_1 = 29 = 2*14 + 1 P_2 = 113 = 8*14 + 1 P_3 = 4454215139669 = 318158224262*14 + 1 ---------- a(7) = 15 n=8 ---------- k=3: 21523361 P_1 = 21523361 = 1345210*16 + 1 ---------- a(8) = 3 n=9 ---------- k=199: 119763748259442622258687159079564739058201 P_1 = 37 = 2*18 + 1 P_2 = 109 = 6*18 + 1 P_3 = 1009 = 56*18 + 1 P_4 = 19801 = 1100*18 + 1 P_5 = 174241 = 9680*18 + 1 P_6 = 18056917 = 1003162*18 + 1 P_7 = 42383773 = 2354654*18 + 1 P_8 = 11146160593 = 619231144*18 + 1 ---------- a(9) = 199 n=10 ---------- k=3: 1743392201 P_1 = 41 = 2*20 + 1 P_2 = 42521761 = 2126088*20 + 1 ---------- a(10) = 3 n=11 ---------- k=45: 1173938396195901909924745559692382813 P_1 = 1013 = 46*22 + 1 P_2 = 19946653 = 906666*22 + 1 P_3 = 58098621688071123199743517 = 2640846440366869236351978*22 + 1 ---------- a(11) = 45 n=12 ---------- k=13: 271400385187185256385797681 P_1 = 1009 = 42*24 + 1 P_2 = 407865361 = 16994390*24 + 1 P_3 = 659481276875569 = 27478386536482*24 + 1 ---------- a(12) = 13 n=13 ---------- k=25: 1110223024625156540423631668090820313 P_1 = 313 = 12*26 + 1 P_2 = 51169 = 1968*26 + 1 P_3 = 537181587281 = 20660830280*26 + 1 P_4 = 129044008326199409 = 4963231089469208*26 + 1 ---------- a(13) = 25 n=14 ---------- k=13: 7751466401331198107634767552761 P_1 = 113 = 4*28 + 1 P_2 = 14281 = 510*28 + 1 P_3 = 4803378460849459680406337 = 171549230744623560014512*28 + 1 ---------- a(14) = 13 n=15 ---------- k=181: 26873686741137134426955168731418493356521556094743907844655852809701 P_1 = 61 = 2*30 + 1 P_2 = 241 = 8*30 + 1 P_3 = 15241 = 508*30 + 1 P_4 = 16381 = 546*30 + 1 P_5 = 4453321 = 148444*30 + 1 P_6 = 11181904117381 = 372730137246*30 + 1 P_7 = 127647229190429161 = 4254907639680972*30 + 1 P_8 = 1151901497068423921 = 38396716568947464*30 + 1 ---------- a(15) = 181 n=16 ---------- k=3: 926510094425921 P_1 = 926510094425921 = 28953440450810*32 + 1 ---------- a(16) = 3 n=17 ---------- k=35: 15750107133630695656454091905907262116670608520507813 P_1 = 613 = 18*34 + 1 P_2 = 3673 = 108*34 + 1 P_3 = 11650237 = 342654*34 + 1 P_4 = 600436865489171456012569882219016103901 = 17659907808505042823899114182912238350*34 + 1 ---------- a(17) = 35 n=18 ---------- k=71: 2209380711722505179506258739515256753910719881144363614772311779761 P_1 = 937 = 26*36 + 1 P_2 = 1297 = 36*36 + 1 P_3 = 87553 = 2432*36 + 1 P_4 = 180001 = 5000*36 + 1 P_5 = 12705841 = 352940*36 + 1 P_6 = 7375572577 = 204877016*36 + 1 P_7 = 1230965509116863530196156369532169 = 34193486364357320283226565820338*36 + 1 ---------- a(18) = 71 n=19 ---------- k=39: 1443527531565015288971659602421654614489642374605083551409641 P_1 = 761 = 20*38 + 1 P_2 = 1896882433068351233865518531434500150446310610519163668081 = 49917958764956611417513645564065793432797647645241149160*38 + 1 ---------- a(19) = 39 n=20 ---------- k=9: 73904414707172961658041605103191648801 P_1 = 8194721 = 204868*40 + 1 P_2 = 21523361 = 538084*40 + 1 P_3 = 700984481 = 17524612*40 + 1 P_4 = 597747428754241 = 14943685718856*40 + 1 ---------- a(20) = 9 n=21 ---------- k=545: 4242512200806304943287553811891982533540837455762603763544422524409634953552627056692585938435513526201248168945313 P_1 = 2689 = 64*42 + 1 P_2 = 148513 = 3536*42 + 1 P_3 = 69785773 = 1661566*42 + 1 P_4 = 26286186697 = 625861588*42 + 1 P_5 = 88223553601 = 2100560800*42 + 1 P_6 = 9714896426474055097 = 231307057773191788*42 + 1 P_7 = 6756948725774425970217675778885509119001021944029069353637 = 160879731566057761195658947116321645690500522476882603658*42 + 1 ---------- a(21) = 545 n=22 ---------- k=21: 7526948986364435360125803495570405163561549104635310045641 P_1 = 353 = 8*44 + 1 P_2 = 97241 = 2210*44 + 1 P_3 = 313433209 = 7123482*44 + 1 P_4 = 715521049 = 16261842*44 + 1 P_5 = 29831330140869137 = 677984775928844*44 + 1 P_6 = 32775913825604401 = 744907132400100*44 + 1 ---------- a(22) = 21 n=23 ---------- k=45: 5581432000155175773629606603896785519251938083584718697238713502883911132813 P_1 = 1013 = 22*46 + 1 P_2 = 76598585809 = 1665186648*46 + 1 P_3 = 71930891189811363992497751749087887268729126225433815568032489 = 1563715025865464434619516342371475810189763613596387294957228*46 + 1 ---------- a(23) = 45 n=24 ---------- k=5: 1776356839400250464677810668945313 P_1 = 97 = 2*48 + 1 P_2 = 2593 = 54*48 + 1 P_3 = 29423041 = 612980*48 + 1 P_4 = 240031591394168814433 = 5000658154045183634*48 + 1 ---------- a(24) = 5 n=25 ---------- k=101: 8223159109219409499609606011921648513809062321064239696037613449848504539113314745425955324806127501 P_1 = 601 = 12*50 + 1 P_2 = 1301 = 26*50 + 1 P_3 = 5101 = 102*50 + 1 P_4 = 39301 = 786*50 + 1 P_5 = 3146501 = 62930*50 + 1 P_6 = 10827505640180401 = 216550112803608*50 + 1 P_7 = 1539826209970662845063693823885188037032677650843152489274354301 = 30796524199413256901273876477703760740653553016863049785487086*50 + 1 ---------- a(25) = 101 n=26 ---------- k=5: 1110223024625156540423631668090820313 P_1 = 313 = 6*52 + 1 P_2 = 51169 = 984*52 + 1 P_3 = 537181587281 = 10330415140*52 + 1 P_4 = 129044008326199409 = 2481615544734604*52 + 1 ---------- a(26) = 5 n=27 ---------- k=1405: 47151065735224384996675736070052561597832597879456799820250947236286802632871980583463274085427461384741270118454816670763576463107941139085710346989799290895462036132813 P_1 = 433 = 8*54 + 1 P_2 = 3889 = 72*54 + 1 P_3 = 9397 = 174*54 + 1 P_4 = 9829 = 182*54 + 1 P_5 = 987013 = 18278*54 + 1 P_6 = 177838326793 = 3293302348*54 + 1 P_7 = 345485598193 = 6397881448*54 + 1 P_8 = 3896772726601 = 72162457900*54 + 1 P_9 = 315747690563007217 = 5847179454870504*54 + 1 P_10 = 187402641521666352553 = 3470419287438265788*54 + 1 P_11 = 2469675755672579423555646824233 = 45734736216158878213993459708*54 + 1 P_12 = 8778655796474774364219502685841752481738585313 = 162567699934718043781842642330402823735899728*54 + 1 ---------- a(27) = 1405 n=28 ---------- k=13: 120170462741932869615842113431673744346085060589569108302340721 P_1 = 407865361 = 7283310*56 + 1 P_2 = 17254637799169 = 308118532128*56 + 1 P_3 = 17075564227260177641438981577201118063969 = 304920789772503172168553242450019965428*56 + 1 ---------- a(28) = 13 n=29 ---------- k=59: 2560864970639256403514700858757623088553245004510870547924901531049454392068953050819953079307623325661 P_1 = 1741 = 30*58 + 1 P_2 = 2437 = 42*58 + 1 P_3 = 2914478065165021 = 50249621813190*58 + 1 P_4 = 49806777187235649295953157 = 858737537710959470619882*58 + 1 P_5 = 4157987191127254667427340097366933288152090785059194189 = 71689434329780252886678277540809194623311910087227486*58 + 1 ---------- a(29) = 59 n=30 ---------- k=107: 28973213417266746048477621111858232850267919602066611010644020276096628509808021483458096184289484159138821238965071497001 P_1 = 4201 = 70*60 + 1 P_2 = 8521 = 142*60 + 1 P_3 = 15601 = 260*60 + 1 P_4 = 90271681 = 1504528*60 + 1 P_5 = 170416921 = 2840282*60 + 1 P_6 = 250753201 = 4179220*60 + 1 P_7 = 2252089418881 = 37534823648*60 + 1 P_8 = 1294794364200481 = 21579906070008*60 + 1 P_9 = 17181861667239601 = 286364361120660*60 + 1 P_10 = 268431577181330387272916793333072634107121 = 4473859619688839787881946555551210568452*60 + 1 ---------- a(30) = 107 n=31 ---------- k=61: 245143157157651285108950829972275373253337648181226211005946579246598297867292904220995426725464638931093165661 P_1 = 1861 = 30*62 + 1 P_2 = 267150983031953 = 4308886823096*62 + 1 P_3 = 22307442560653759601 = 359797460655705800*62 + 1 P_4 = 933383285855323028339877431039256733 = 15054569126698758521610926307084786*62 + 1 P_5 = 23681369939410957536563854367119676749 = 381957579667918669944578296243865754*62 + 1 ---------- a(31) = 61 n=32 ---------- k=3: 1716841910146256242328924544641 P_1 = 1716841910146256242328924544641 = 26825654846035253786389446010*64 + 1 ---------- a(32) = 3 n=33 ---------- k=5369: 744619946863588235834351706979256906238196748702139493828387949798971193106291385785995680637442423654815393314241676989474140979893247762355212012702101913979213601301759668710724733812147275774342053642996208160878495577550901401833507337558041 P_1 = 127249 = 1928*66 + 1 P_2 = 14413081 = 218380*66 + 1 P_3 = 52430614509769 = 794403250148*66 + 1 P_4 = 195648126278617 = 2964365549676*66 + 1 P_5 = 830947529171761 = 12590114078360*66 + 1 P_6 = 97510899876452425631269 = 1477437876915945842898*66 + 1 P_7 = 7555846323546661308432391736800418608539323544330971969367529 = 114482520053737292552005935406066948614232174914105635899508*66 + 1 P_8 = 64647679125771533464812439572653586773617841359092032475585442039817358587117162444747447407024976644875013 = 979510289784417173709279387464448284448755172107455037508870333936626645259350946132537081924620858255682*66 + 1 ---------- a(33) = 5369 n=34 ---------- k=13: 2799741670169483507698486708728734483268191040098775504673153759149236287561 P_1 = 137 = 2*68 + 1 P_2 = 409 = 6*68 + 1 P_3 = 14281 = 210*68 + 1 P_4 = 63104137 = 928002*68 + 1 P_5 = 55444393239496164406865681531894115168657269299195964355161 = 815358724110237711865671787233736987774371607341117122870*68 + 1 ---------- a(34) = 13 n=35 ---------- k=7069: 142570187455546254353202109587020527689532400767535017664109158740774486775206739398446752143840097527265928945281648797238738108988041630026902248396197158091425711366273483821789956116805549437637147336439090709866750945717019385306312983778988743155310192822977684301 P_1 = 24985381 = 356934*70 + 1 P_2 = 5751719867885102932241 = 82167426684072899032*70 + 1 P_3 = 594261219200137133847721 = 8489445988573387626396*70 + 1 P_4 = 6235393194007316635125386539921 = 89077045628675951930362664856*70 + 1 P_5 = 736733012191435663431544056302281 = 10524757317020509477593486518604*70 + 1 P_6 = 15570256649615202104821628502171610482542758681 = 222432237851645744354594692888165864036325124*70 + 1 P_7 = 23339840416190588810174421964442990994901361049094988978077411853472124368222500257535550047508968571554081 = 333426291659865554431063170920614157070019443558499842543963026478173205260321432250507857821556693879344*70 + 1 ---------- a(35) = 7069 n=36 ---------- k=305: 37030402899778008934610078295359728875374199072356247500960521057468371482917856747584319791472759593993050414199997410633041355608914828746042191554010969412047415971755981445313 P_1 = 1297 = 18*72 + 1 P_2 = 2161 = 30*72 + 1 P_3 = 36433 = 506*72 + 1 P_4 = 1516897 = 21068*72 + 1 P_5 = 116112247977601 = 1612670110800*72 + 1 P_6 = 37442834569781445313 = 520039369024742296*72 + 1 P_7 = 535383147036458592671880654769927637233 = 7435877042173036009331675760693439406*72 + 1 P_8 = 5607863442480081883456821020466150000001 = 77886992256667803936900291950918750000*72 + 1 P_9 = 18314867876452579181177494180783234248169518582241 = 254373164950730266405242974733100475669021091420*72 + 1 ---------- a(36) = 305 n=37 ---------- k=221: 152755992762820070149076248657921381179549873291923316458583550704822740382988684571156068696558512437126680223464837222678436879489831479529870210944200393605398347184028341 P_1 = 149 = 2*74 + 1 P_2 = 10657 = 144*74 + 1 P_3 = 24421 = 330*74 + 1 P_4 = 3939250322328015540241969538844550373949611831252878022707212691239534463896718697741430725756948031082708186610558865328303416618757343850606417590898071812684397 = 53233112463892101895161750524926356404724484206119973279827198530263979241847549969478793591310108528144705224467011693625721846199423565548735372849973943414654*74 + 1 ---------- a(37) = 221 n=38 ---------- k=39: 4167543468772372422904529812968146836645152612072606301219722957670804753621706248019658422679589891999194115829272678481 P_1 = 1217 = 16*76 + 1 P_2 = 44537 = 586*76 + 1 P_3 = 1156721 = 15220*76 + 1 P_4 = 380121424810577 = 5001597694876*76 + 1 P_5 = 58916353431905811424543698977 = 775215176735602781901890776*76 + 1 P_6 = 2968122170917490932615204576356053901392169805854830955175776121 = 39054239091019617534410586531000709228844339550721459936523370*76 + 1 ---------- a(38) = 39 n=39 ---------- k=131: 701667022163438448327128215771657149330504075480884112304405966450535408748025561002748753869946328572711444054849785160721044636205129561041237592789978822312991421 P_1 = 157 = 2*78 + 1 P_2 = 8581 = 110*78 + 1 P_3 = 9317257 = 119452*78 + 1 P_4 = 294482761 = 3775420*78 + 1 P_5 = 59850507787909021 = 767314202409090*78 + 1 P_6 = 150589338791947630537 = 1930632548614713212*78 + 1 P_7 = 652357694798659018095976526956267447007258013664561 = 8363560189726397667897134960977787782144333508520*78 + 1 P_8 = 32284770585421126863081565557183011923177336744744677577 = 413907315197706754654891866117730922092017137753136892*78 + 1 ---------- a(39) = 131 n=40 ---------- k=3: 73904414707172961658041605103191648801 P_1 = 8194721 = 102434*80 + 1 P_2 = 21523361 = 269042*80 + 1 P_3 = 700984481 = 8762306*80 + 1 P_4 = 597747428754241 = 7471842859428*80 + 1 ---------- a(40) = 3 n=41 ---------- k=165: 34092074583129200170965481324600300291216355286626951504452925032025099849047419784897420979172963680904781193512175810025961327269252577724673730630300383381836581975221633911132813 P_1 = 13613 = 166*82 + 1 P_2 = 2504376300824887987289023824623543692883005603954084441669942336885704829871991462932301548459043831697993182510260472344520776263075925785989402088466934796285652095439773298401 = 30541174400303512040110046641750532840036653706757127337438321181532985730146237352832945712915168679243819298905615516396594832476535680316943927908133351174215269456582601200*82 + 1 ---------- a(41) = 165 n=42 ---------- k=169: 6941497824485713665512951965938654325484435723673617802605679078626074260831159005338040361509879576910752445690017599060423270092173269314080952193895499172523360874699646912292892724561 P_1 = 1009 = 12*84 + 1 P_2 = 407865361 = 4855540*84 + 1 P_3 = 16425059281 = 195536420*84 + 1 P_4 = 17254637799169 = 205412354752*84 + 1 P_5 = 659481276875569 = 7850967581852*84 + 1 P_6 = 17075564227260177641438981577201118063969 = 203280526515002114779035494966679976952*84 + 1 P_7 = 5285120289443207164220750356636306694046792083280352749380327392017146438302272512484318769133041 = 62918098683847704335961313769479841595795143848575627968813421333537457598836577529575223442060*84 + 1 ---------- a(42) = 169 n=43 ---------- k=85: 4255960766459290728516547375043452827240555308848190185994891954555515831209090204521989391986267718301310804689089086910735743735090252926056564319878816604614257813 P_1 = 3613 = 42*86 + 1 P_2 = 83077 = 966*86 + 1 P_3 = 197664121 = 2298420*86 + 1 P_4 = 7073999734649 = 82255810868*86 + 1 P_5 = 3797823768224242144447132239150452732507796462601 = 44160741490979559819152700455237822471020889100*86 + 1 P_6 = 2670060832236458352507808261342737744953913831820529761718686478329597671902318649013997 = 31047218979493701773346607690031834243650160835122439089752168352669740370957193593186*86 + 1 ---------- a(43) = 85 n=44 ---------- k=43: 278095585774086836786321591602231627810788360000927721170417548972813674058291235578337845045517657414444613358388580052792227651686095819926801 P_1 = 353 = 4*88 + 1 P_2 = 9857 = 112*88 + 1 P_3 = 5844100138801 = 66410228850*88 + 1 P_4 = 268403319303834417649 = 3050037719361754746*88 + 1 P_5 = 50952922876799967137900554113297115418602660177927920151043914561403222496872997183813849131480173021969 = 579010487236363262930688114923830857029575683840090001716408120015945710191738604361521012857729238886*88 + 1 ---------- a(44) = 43 n=45 ---------- ---------- a(45) = ? n=46 ---------- ---------- a(46) = ? n=47 ---------- k=95: 402706742914834171037415318541704946787412887212777910756031892462937415492730412401540677651218823570072805747008545449548873932564104126241154735926786045752123754937201738357543945313 P_1 = 4513 = 48*94 + 1 P_2 = 220648081 = 2347320*94 + 1 P_3 = 18790439262426329 = 199898290025812*94 + 1 P_4 = 26325255306074609 = 280055907511432*94 + 1 P_5 = 5130223472675451765706474913 = 54576845453994167720281648*94 + 1 P_6 = 159359370471779354433492434633847089381287980671458782421864208056919579854951087003575713579411151087102622949897 = 1695312451827439940781834410998373291290297666717646621509193702733187019733522202165699080632033522203219393084*94 + 1 ---------- a(47) = 95 n=48 ---------- k=19: 287949080341050116418140552378595512384972258634101709618299713530825733751958841909016642608985561598556704813017211791041 P_1 = 193 = 2*96 + 1 P_2 = 151681 = 1580*96 + 1 P_3 = 1954753 = 20362*96 + 1 P_4 = 5502533014277739311301121 = 57318052232059784492720*96 + 1 P_5 = 274254682725217636458847635846091201 = 2856819611721017046446329540063450*96 + 1 P_6 = 3334406982445127458321224533542354534333731184129 = 34733406067136744357512755557732859732643033168*96 + 1 ---------- a(48) = 19 n=49 ---------- ---------- a(49) = ? n=50 ---------- k=851: 49195571806275450621956474844627515715666199104998327691554524577027954771029128618721636664170859738571577449244844414802981992308513912947453951858158373537888597361668488592226992887620428822266007495146594304638857393114119908548004582689397840563994606248954489227704510894839857622605001 P_1 = 2801 = 28*100 + 1 P_2 = 93621401 = 936214*100 + 1 P_3 = 3337940695655201 = 33379406956552*100 + 1 P_4 = 1788517276110359967422984253001 = 17885172761103599674229842530*100 + 1 P_5 = 11275945308028165089764062083623201 = 112759453080281650897640620836232*100 + 1 P_6 = 44425920006169668887728579702677168122801 = 444259200061696688877285797026771681228*100 + 1 P_7 = 75661154068572347029331080513188908237504416801 = 756611540685723470293310805131889082375044168*100 + 1 P_8 = 118901050892012905170153561161053433395395334601 = 1189010508920129051701535611610534333953953346*100 + 1 P_9 = 6972972728910847901399136114950472544540867509557488926821938255201 = 69729727289108479013991361149504725445408675095574889268219382552*100 + 1 ---------- a(50) = 851 n=51 ---------- k=6425: 12648221679721403931506674513825816409235051407649289021446417615850262503186736568881754366096867920474509306314775793121743049821758677157904591836196419598954361462008929049698905572155463402987635669198573415185016002072085058232829806032973489922082638728114405310617505755319752443195235151999085064529360421364945986179274993457811738667179602552126382875030685681849718093872070313 P_1 = 20640313 = 202356*102 + 1 P_2 = 35037590092237 = 343505785218*102 + 1 P_3 = 1704089959110001 = 16706764305000*102 + 1 P_4 = 3202185257060036534124057005053 = 31393973108431730726706441226*102 + 1 P_5 = 37699683718177035800760792875809 = 369604742335068978438831302704*102 + 1 P_6 = 71111561238902898920791741101583175409134548311039012217914828657031902590857789028247080614579214973991101065656365360001 = 697172169008851950203840599035129170677789689323911884489361065265018652851546951257324319750776617392069618290748680000*102 + 1 P_7 = 1195534383370171892408679512547913551585006772605782869325434208324168952494564345425409094174777930073102581929761463357587686992554833873261520056270150568540253376649 = 11720925327158547964790975613214838741029478162801792836523864787491852475436905347307932295831156177187280214997661405466545950907400332090799216237942652632747582124*102 + 1 ---------- a(51) = 6425 n=52 ---------- k=47: 395500675552793007656534901006971755552840199201915465472011719200369097475131619887598321820494664824927456192110478784612201617306086963734197812020036657524673162729675841 P_1 = 3121 = 30*104 + 1 P_2 = 27809235793 = 267396498*104 + 1 P_3 = 86561886529 = 832325832*104 + 1 P_4 = 11905643330881 = 114477339720*104 + 1 P_5 = 2657692249060624084162536990981589230938059553377 = 25554733164044462347716701836361434912865957244*104 + 1 P_6 = 1663719611497887290539557443388784653491386299069794263216976811063374810613245628350689 = 15997303956710454716726513878738313975878714414132637146317084721763219332819669503372*104 + 1 ---------- a(52) = 47 n=53 ---------- ---------- a(53) = ? n=54 ---------- ---------- a(54) = ? n=55 ---------- ---------- a(55) = ? n=56 ---------- k=29: 30728811901214145575588153802309529626167715630562648516475863613813402479945679848901405173127384792364806895524710720728143248061384770057752329651854810915175521 P_1 = 12097 = 108*112 + 1 P_2 = 4060897 = 36258*112 + 1 P_3 = 125123236840173674393761 = 1117171757501550664230*112 + 1 P_4 = 61488253575510632263280090712701231035856609 = 549002264067059216636429381363403848534434*112 + 1 P_5 = 81304762449964713098732970074199421701803635181833250945475956834009234249456617497281 = 725935379017542081238687232805351979480389599837796883441749614589368162941576941940*112 + 1 ---------- a(56) = 29 n=57 ---------- k=571: 90258132691923642084635375161218311120222886583328078123734351428902385708922164712403741004148487185586078694891975354659970699312318018800605767416653627781358298890193075576948747418209302766420485920459179227427366238321826110868801290822490115269769398995103220756445230877668642526414645184647983833366728941 P_1 = 229 = 2*114 + 1 P_2 = 4561 = 40*114 + 1 P_3 = 163021 = 1430*114 + 1 P_4 = 13779015157 = 120868554*114 + 1 P_5 = 106302407641 = 932477260*114 + 1 P_6 = 711887704861 = 6244628990*114 + 1 P_7 = 20611820761943941 = 180805445280210*114 + 1 P_8 = 89505865925913498812041 = 785139174788714901860*114 + 1 P_9 = 974117472920642898985656941379217612167097 = 8544890113338972798119797731396645720764*114 + 1 P_10 = 163191190956851286761273349091908854086969802200535720430474261922590543515599199522560681 = 1431501675060099006677836395543060123569910545618734389741002297566583715049115785285620*114 + 1 P_11 = 1733399092380761665115096022227644982261754491983693863530387609377536436834337444417685168582519961 = 15205255196322470746623649317786359493524162210383279504652522889276635410827521442260396215636140*114 + 1 ---------- a(57) = 571