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Palindromic Numbers
beyond base 10 Page 3
rood Page 1 rood Page 2 rood Page 4 rood
rood Sum of First Numbertypes rood Sequence Products rood Reversal Products rood
rood Pythagorean Triples rood Palindromes in Concatenations rood
rood Various Palindromic Sums

b2+b3 & b2+b4b2+b5 & b2+b6b2+b7 & b2+b8b2+b9
b3+b4 & b3+b5b3+b6 & b3+b7b3+b8 & b3+b9 
b4+b5 & b4+b6b4+b7 & b4+b8b4+b9 
b5+b6 & b5+b7b5+b8 & b5+b9  
b6+b7 & b6+b8b6+b9  
b7+b8 & b7+b9   
b8+b9   

Introduction

Palindromic numbers are numbers which read the same from
 p_right left to right (forwards) as from the right to left (backwards) p_left
Here are a few random examples : 7, 3113, 44611644

  1. Go directly to the Simultaneous Palindromic in two bases topic
  2. Go directly to a Base 3 and Base 9 topic

led Simultaneous palindromic in two bases led

Index Nr

Simultaneous palindromic
in base 2 and base 3
A060792

L equi 10

L base 2

L base 3

Next > 2^188T
213062203262076400001613703360727584839894186255489940581756185117
2067671017476698724526418868663742431005722899409952160754179113
194246885778661648668789116570919163465391339378554490353175111
189381483378275268348628619470726203136854296294348950167105
17240149989633833026009551628667871536524440494414591
16323456844917032449804068807044799066420454113585
15304126381621992512735097581277303000261894113585
1415978632432064038577872469205445229123614013183
134280273360715972540249227931072185959733912981
12324568363047752044399122312019662547873812579
113926296215822226677332139070541160733611975
1080225810575338237618294366620993110365
92004595370006815987563563258151
81922624336133018996235227145
7381920985378904469185937
690396755477113723
5541558972315
4142277372113
366434139
21111
10111

Index Nr

Simultaneous palindromic
in base 2 and base 4
A097856

L equi 10

L base 2

L base 4

 

Please refer to the OEIS b-file at
https://oeis.org/A097856/b097856.txt
The list is too long to replicate here.

Index Nr

Simultaneous palindromic
in base 2 and base 5
A182232

L equi 10

L base 2

L base 5

Next Q ⩾ 77Q
78229043041754405769330851403502285402839704672204869595317475
77228005284752105289132526059623967101029764461043885595317475
763491883348508605358523437928520148249464442845407915116873
759031558794294247293178449835590824677008877354174816069
746255125538204705505254235834855865974894713581714815969
733473815566660782666347665618207474579886886847514815869
72265311683808467113018305119713786330140813837214715567
715528519079657779307911062588313758348601452514514965
70712586910486729092993630607216985049950456834414663
6925667675190511456211785857920538432948218474314161
6825154222198803837075053274035986243792734474314161
6724121855558215487607066938176600229457678674314161
66Prime!    17864014337156170324684867642570119897702774314161
6517268796308779601849974231137622248682561214314161
64426011455073753962411529762028187136016314113559
63387866042802604810899301263209871909805514113559
6242588905376854375594609355547233600804034013257
6141940607243985576705288765048610171240034013257
6036142563220661416071989250812516866825174013257
5930528661475683885947456620123553751249774013257
582097224218270401720044652764015451759933912855
571778523596419815068587977385314725856333912855
563757971579119657898879500433530560093611951
553210170372269199263761878167667801433611851
54135906299457784874396685444766847733511449
5341357054562211183887272825742888513411249
524254379341091699778907422653449973310947
5193349441187646239944464991287913110345
5077597076496730000177661733457313110345
499887588756301085036055272954593010043
4838652107687766448554875360159299541
4724128895953661106298526611417299541
4615158702466911667284152932291299441
451057658684466420673381657947289039
44736745530518950421460900377279039
4334083641094041215425827207268537
4230101157511305300778061027268537
4120563671288597289812895761268537
40105531909578180191904589247733
3927166507811241546115101237533
382792665749769510987497227231
372536733867455442723217227231
362449913965194573706017227231
351999022506621150444827227131
341849130200000590372371227131
33150319808235063576129216829
32136329883505815551543216729
31122932536640098304683216729
30120110524940556687883216729
2989701695563295218137206729
2873819093863158149121206729
2757338685589431482211206629
261705198171059456701196127
25267590170057856439185825
24202124162283446733185825
23151875068667242337185825
2299805500812710541175725
218829547069230943165323
206299497017331917165323
194738749440161121165323
182996750083037781165223
17286118927218753154921
16567897922593124017
15169179279801123817
1426777829859113515
1317935304097113515
127609865031103315
1134013498192913
106823416209
95208316199
8389375167
727094125
6119373
593273
4Prime!    31253
3Prime!    3121
21111
10111

Index Nr

Simultaneous palindromic
in base 2 and base 6
A182233

L equi 10

L base 2

L base 6

Next > [207]
2071529429269693953505685233122491030591556210592649745053268281576320780
20684864692214185143624741416443952653355954699240517003573327576120379
20584492616883862114219938560919907627694506906260354598100341976120379
20467760283156159095077850554723147731239902551523124401709361616120379
20367689703481766024854301701506373429790086737802784590338998736120379
20267606296346093768819542291997613599607367885790153374935954896120379
201135748808246704579357251283772506889484573936206471207378736019475
200135748808246704579357251283772506889484573936206471207378736019475
199135748808246704579357251283772506889484573936206471207378736019475
198135748808246704579357251283772506889484573936206471207378735919475
19764771216176765042734212330852589622956217978384105154908495819375
1966210522386919586015912392670678905783244855364492384679235718973
1955398698398525353473824678995597857022244709641076563077255718973
1943563148259916315403482225329227028595823115781213463186155718873
1933326774437885508545421602133657860448390066155393814795795718873
1923325247451357149763446385584931633315871453908447716882195718873
1913274034742161854827699270247529720896183775567712994031795718873
190634776828871195147540259632222935594015312945735970953335618672
189254326379999494878629041381314341907020115388898799624015618572
188112882116044669869655782290150721665309912362074430949995618371
187111486569950586070161615184307502568729362150728064581355618371
186109348087432957670556591364897489222157851063134596736395618371
185100031617316912295018083996426284509980644145283252897395618371
1846245860807342052220078173132049316890394837143146877555417970
1834173403351441027224746631725592432032472190437376959535417969
1823031946673945591140379098400074852349442753983562325315417869
1811406611535236619089055289080027925332048470521395527335417769
1801199998562743643645546351678536063260348027339555292215417769
179432521806819837613140406903500244351253586114000437515317568
178118534994456236645512685896734358293719121538118980475317367
17782662096822199675236355620955741991045300222870151815217367
17681258372198393980258862891333934636099386710430181655217367
17575503244363698323744877624900864667482227204363751735217367
1742529774070446976791851690904925462043792523882723095116865
1732486360025998822631656007684663518032635416746373975116865
1722446063406321050513618705819932376331651267273510135116865
1711061578603104798377042926456792469329767076461042015116765
170394832819311960453776345883412348231814768731074835016564
169337328020889920466736831144351908850130180509299495016564
16897426925115643309689560133481548951177951459109554916363
16769500751284508835006455634284401781303344188098814916363
16662361592278154452425998241702717227003565031631534916363
16529100385716344456831598425035087394022145682789114916163
16427273149484027646164440054710023762016936846447274916163
16311121208381834151417203939988425967129709938409634916062
1629738084560297251693605979052075706238556549143894816062
1611902976694696544613426254473332355377442072275534815861
160263841600615844493697911622657061766065620766174715560
15951056376385791389858996503068762694674407462794615259
15819667537741583157075185464608193707524121083014615159
15714648714757252117110677645620150434623098702734615159
1568029964132801489957069978822838866101238415454515058
1556867803665028746556562498932038747840438257754514958
154441759723069675845658967985199082907308814714414557
153225889815140989161854024997205092264880305934414556
152210906529230109615569992051401509102165586714414456
151198522752728427167626653062429362639324548554414456
15072377049071083578228593481898699839540317174314356
14940635944452338850729553482849225770655358374314255
14840635188108166254065340975546342392761163174314255
14740617514978729456618821092683816188073414054314255
14634880764926972080635984867521393418664888374314255
14514387489403438195123104230684459969886955854314155
1441707339884209157862502291391890952342393274213753
143958550983763655354909555478222265430249454113753
142352120622106388538084713387371781798419074113553
141321962261880769096270978542315425433427814113553
140184175368355749912463499579881972177956114113452
139158809548311182036187316743965610890007974113452
13893506076611697129223443379725954831595154013352
13732072406767058130561058871789003989123614013251
13629067165122881083636920055407515613401774013251
13524652971653583074350137594825641041377034013151
134Prime!    1339574980462081786081720585085707513793912749
1331127679267718204162562965772736442669013912749
132847237951302470908011715579784396266233812649
131147068454907521548627913149901941884293812448
13068196015262273349276323444110687406453712348
1296221673950135290051406388335937059753611946
1283694848946973026972710549572141901933611946
1271198793444794427187930634326643950373611746
1261079139835837490114899238942461876213611746
125619493043280590892132437539646769893511645
124554894430804040231815472461601012053511645
123336524625240048839607236525605782913511545
122297285516398118229768036145959354693511545
121295453376546450566341303288145122373511545
120238392591204912060103090877412042973511545
11917397437324895286230002245715030613411143
1182790085628401548302349158608138833310842
1172496368535696372769580090111895393310842
1161261753411841868069160050131949793310742
1151261467388736042873771286741895393310742
1141127262820061840033346950929847173310742
113811871695105785679617092472606733210742
112533926783847270459913909076208853210641
111432300656760243387489413842263213210641
110230982216609219384305825756373853210541
10921882153975161953882094342101073110139
10819240035403225102299113955251873110139
10712463097792335130255084736383673110039
10611514609919587647617213213289193110039
105594057412834676046160977203191309939
104590250036124062960060569380471309939
103Prime!    493729853550986902109639562979309939
102335090923209477962166023351009309938
1011071558545897407097590245819289035
1001001420152774788863902968051289035
99Prime!    540770568795997877440747003278935
98416236030633502957919626293278935
97400653544480402135930580389278935
96398732494354320733571553061278935
95185917164959453833657750425278834
94171662799836802452809646001278834
93156780573668704785535726977278834
929357001767213361375852015258333
91802965820999708024967253248031
90704230003987273379873961248031
89316606603738187666909281247931
88Prime!    34579344526412674075223237529
8733783643594880314423079237529
8624207503363570422943781237529
8522419218190317444716521237529
847840845872292061995307227329
837503607230677085144787227329
826666318737698860764461227329
813574872687181455610755227228
801407478774388559878425227128
79570868485923851782639216927
78529106159925017013927216927
77514888825293028733691216927
76307741857092771540641216927
75297229306823447209729216927
7417836907961939038703206425
7314606792210184908115206425
72Prime!    9027418797989294431196325
716851803640999392381196325
70442782624909444387185923
69421678237970776797185923
6866914369589632439175622
6735031040848860959175522
6625318737011894221175522
6524109374625379029175522
6413294033268299581175421
6312825774359298669175421
6212141647369392437175421
6111931182927622549175421
606636395485755709165321
596451588843354861165321
585214602113362985165321
574978544622304945165321
562040316732420071165120
55535608924080591154919
54Prime!    129956651976247154719
53125823357614887154719
52121593745290427154719
51105026120405245154719
5062995659142311144618
4959238470140395144618
4827303621891427144518
4711214404390085144417
4610982103577593144417
459154514971809134417
44305975844465123915
43276893011713123915
42262273188399123815
41243737427783123815
40129132454159123715
3984408212665113715
3846499142837113614
3743253138565113614
3619435516681113514
3518805635121113514
3417807619361113514
338632935681103413
326662648163103313
311894216583103112
3020808048392811
293064309582510
283052213582510
2719861277219
2619740317219
2516329957218
2415083817218
2310932817218
2210403197208
214259716198
201802136187
191535136187
181514976187
171486176187
16Prime!    850935177
15664335177
14285395156
1345934135
1242574135
1139994125
108193104
96933104
8427394
7129383
621252
5Prime!    7132
4Prime!    5131
3Prime!    3121
21111
10111

Index Nr

Simultaneous palindromic
in base 2 and base 7
A182234

L equi 10

L base 2

L base 7

 
9111455626731165907019510815560846173168308108244540835217061
90419021384949328808524653371528244974502125674646155016559
89404022784949094064255814519731602091861831365357395016559
8813768533031630168627178437338385271679970105232794916057
8711745168359541185744367589337893057216630418876674916057
868228459180663165367789196101135370485508502661214816057
858060505052043161252021780643183009652909403700974816057
847499825662045492039351708379600033450178950253454816057
836220489596765447153248885404863798990236729240594815957
825935383306872358248919023128014989665836116520834815957
815137192234445420721846664937076892298772516658694815957
804172009615770969865918690816730223882501027195614815957
793037505429777891087007891939278449730110499909554815857
782769190038372482120327039419966120428587381965474815857
7795163607158233804293425086148176144028567292594615355
7664274975306236801171610735749301581885347082334615355
7549852845223713963761433977094558631315994178514615255
74109773043345016105861141172353455646742528634414351
73579074729467479087681912911224028851866454113649
7221354840824566423214838376405339036413634013147
718762240766867279861540310652989455204213913047
708106095211052140444434893802360216407293913047
69750455754733795652457705638496546763593812645
68417916979362540786657673546487070970553812545
673229689364131698357594996284760031033611843
66233618091847732786642166903507763053511541
65191336057460739208473729421437122153511441
648127614144730689613637017497482293311039
636567273960710278527741301181730573311039
625997972986484003289985681121713193310939
615228450626681994097111565386128513310939
602541687968275338170671781169728193310839
591766009114180957017230878547668013310839
581712266678787307143280905766361293310839
57173655956282482723468842559705233210437
5689770726395519624377427243318473110337
5581217321049875141492223864096513110337
5471824994345690978072718241921733110337
53287315133314320447252596189207309835
527168548605154403876853428893289333
517034236954094638601879235501289333
504982557678672427887940064001289133
49Prime!    2059577471782805986901831467289133
48144735146046030299112771319278731
47128713543915362867228053291278731
4680347901032433196717127457268731
4552309532921196512044107957268631
442746522115529753005549193258229
432537709652845469133838945258229
422045328483160276032385307258129
411617042324003877388578005258129
40471678638661546935436259247929
3926432962459781879544013237527
3819855989195900063134049237527
371051742679496162996263227025
36839909381231478441069217025
3516675608147319445223206423
3413694840704790671485206423
338979691592773352607196323
323997451286601328571196223
31427510260590336957185921
3081590995511342857175721
296496728596849949165319
281797708850136627165119
274713161675921134315
263425211644643134215
25Prime!    1566399158893134115
2472822171105113713
2371859215265113713
2237344016593113613
2124051338445113513
2015935958711113413
191052109663103011
18224683098259
17199928578259
16129168998249
157864356207
145126076197
133991716197
122100996187
11117575145
10112535145
992014145
850494135
7Prime!    257393
6Prime!    107373
585273
4Prime!    5131
3Prime!    3121
21111
10111

Index Nr

Simultaneous palindromic
in base 2 and base 8
A259380

L equi 10

L base 2

L base 8

 

Please refer to the OEIS b-file at
https://oeis.org/A259380/b259380.txt
The list is too long to replicate here.

Index Nr

Simultaneous palindromic
in base 2 and base 9
A259385

L equi 10

L base 2

L base 9

 
97305583523420813607217123846142282797160705932374715549
96279343821408219653671631212508550035590471867454715549
957045668674055253597724041945546433278359642234514947
943959728103623138964134582101869982438272656494514947
933640467147773183162816685672316692561064164494514947
9282870905620323277217323320993403266183174374314345
9137082023273677445776716293790805327461504854314245
9021789962117024348323387679539212808764682434314145
8916122728627164307211541187205957212036157854314145
881014612125564200064931897417190218744895134213743
87742395954557652576939491484606670353091474113643
86469556291142450247381392189556745011690414113643
859409491312931300099299929869488226711173913041
845733878458117340623589072635112066226993912941
83104941142018348773008578928861416830073812339
8298115475607761424916457381338762557993712339
8193928436056698415455911626720492892873712339
8091348790147679091660457126125969305233712339
7982465824837548681511781399440307572193712339
7825738203426425314687262663423626843993712139
7723736904885913172488668446352033569673712139
76709454116701244256683285856251067793511637
75Prime!    20737225734065683988372179622456833411135
7413633243954866076184123017373261773411135
7310842698423254530093394637580973233411035
729325122374896404364700177952870213311035
718781060020068409248090140327743253311035
704586130474150885386300782579648453310935
69273838546599920907089534381289493210533
68132995259899535663054818498795253210433
67117619424395701815498855336627613210433
66325449036571496430311934611137309931
65285495032903907768492672121191309831
64272636470146897683727270796347309831
63267330408442281785103076380651309831
62116284153520275827942053886941309731
613313349624824059206539399893289229
603226473616825253131676840805289229
593159242546300009927048702661289229
583141152420006093352888116805289229
57Prime!    615850986357618363622206847278929
5643204338966326005406289777268627
5536331649733825849480459791268527
54Prime!    26315683709701629860193397268527
538969756245665011874576055258327
52566416282712155854161911247925
51536614912484872949318343247925
50287582669371604651338191247825
49250650845788990615646763247825
48242738940902894032509363247825
4724144136782991615395461127825
466080900468847014660901227323
452189299497937221630647227123
4486214274421074129321206721
431306688242829641865196119
421247103797940661841196119
41586178871768257601186019
40487154413087025691185919
39349013080305074009185919
38155315813368497154815
37124537880318279154715
3682474703167593144715
351616662113341134113
341085079274815134013
331032991588623134013
321030890430479134013
3128829406059113511
3025726334461113511
2925636651261113511
2824523959661113511
2711022828069113411
266080408749103311
252711148819299
241349788179289
231336380159279
22Prime!    903521818279
21674726418279
2042109457237
1935193397227
1821221137227
1717869717217
1614053977217
1512451617217
14424055165
13199295155
12Prime!    194335155
11170575155
1066434135
9455393
8273393
7255383
6Prime!    127373
5Prime!    7131
4Prime!    5131
3Prime!    3121
21111
10110
 

Index Nr

Simultaneous palindromic
in base 3 and base 4
A097928

L equi 10

L base 3

L base 4

Next >10^40
57214380839254234655440889874941132677450398164
5648176427308328347699507778889941479174387963
5544472276530120979145866046985726596946387963
54276337661018987462687495864690101015367556
5359474690271450308586281402122719710357358
524419237254320829849524526023871335347156
51759012471444656545609985788546646336955
50679607280480045762110859232530578336955
49641619571827978969545034390725309336955
48493314325578533699770039939408201336955
47477615138809703953510007022636213336955
4669324330723059709731924726447783326753
4543388638498221002798187927595810326551
444265077503410661435679037658583316551
431025231027120608981173243011315316350
4212757893341488272130806455066295947
411158660778387582489404090107285745
401119738295781227187877556955285745
39140149905089671197854759885275544
3815342669176313576547135715265342
3714251811144348961469429310265342
36174949411464869472111638244939
35151289716815885983700994244939
34121904971169450717561305244939
3313267978780025510037454234737
3212419161437212369154346234737
31186471757709076102730214334
3031181788464224909369204133
292330173277374473538193931
281914006557036313769193931
27244091990257709863183729
26193201488006948586183729
25183016579474682506183729
2446991827781783450173528
2337707959614889810173528
225158488358367585163327
212887846891280410163326
201956592840355065163326
19534479689454189153125
1855988454554339142923
17Prime!    53903615484947142923
16635913760790122520
1577887660577112319
1446746179770112318
131136307905101916
1295661365991915
1191682167191915
101143545081512
9Prime!    118172971311
874947061310
71758506119
611950597
5130354
410232
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 3 and base 5
A259374

L equi 10

L base 3

L base 5

Next >10^40
853193156444804097678980914973672565877182408357
843122737401814098051317214506228960128907408357
83234484874714320301124704437182720953509398155
82186186384479839078710563785227785488708398155
81140705550899095073621529622743479302712398055
809347420880258935492931551048502203884377853
793874150642506089623309179674753069216377753
783700301558940565336230758027186929166377753
77407787223690836019209356178116306114367551
76337640314862414423368271377010684398367551
75281969044732536111647611202001002728367551
74267141960244320726956163073287921253367551
73136983023194851653941614777272405336367451
7213499370674725123919625214721421868357249
717269990017523424642017382636233152347149
707078322413240812098152774070159996347149
69Prime!    635730140688854381713947926325539336947
68380813551428217937685319797984292336947
67213596377894346205963141663680936336847
66178460688215552617022863039015156336847
6514788387235488337544459425781892326645
647261385687730490931264802333656316545
63959030355589505562758307094634306343
62758029379825147963952378620833306343
61588904426539734014417353667987306343
60573626404720313270032340775712306343
59359082849107933078822956954736306243
58333606111528080715379480548536306243
5725634071299382641576318335272296041
561342044022128899326901650193285739
55640985782336772789563675741275739
54640283834536373649253906216275739
53482691017369092830404474456275639
5231290540575858153624967952265437
5121561926939038211763219436265437
502855415541113186609997324255235
492163522239611873525643068255235
482072556502296995148346988255135
471708931826852220300687097255135
461108752440124277139412946255135
4576264883561776274379908234833
4432035371021240853343356234833
4331557988159203994267456234833
424611589421840328434224224631
412313109014064895895062224531
402072261080808910025382224531
391363633951126304641036224531
38105734861679582249272214229
376309131572703144884194027
364962844393339522708194027
352195151134400744286193927
34234679042329212848183725
33198586101776613958183725
32187908509573113078183725
31149954769917489312183625
3076226057197381156173625
29278737550525722153121
28158312796835916153021
2718432110906024142819
26670919564984122517
25478999841578122517
24201241053056122417
2318814619428112215
2212814126552112215
219256436186102115
209012701786102115
191065805109101913
1832078555691813
173327438881611
162771177281611
152651369281611
141475293681611
134375766129
124231766129
11678345117
10321525107
92188485
8Prime!    1667475
71066475
652243
526233
44121
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 3 and base 6
A259375

L equi 10

L base 3

L base 6

Next >10^40
11198466203104854439168465249689877383484388049
11098133997882074558158949529616407746628388049
10929223179163812020030867495297920039343387949
10828164669568006439706598264319779387075387949
10717790064827722034936924717405511805944387948
1062502826660057608670977394101167199700377747
1052501272231450190121324330414864101956377747
10483388278106313524478749756728798056357445
10383388251188044394345369799632034920357445
10283351050034645385470322112334272120357445
10145517258868305770790045115577495644357345
10045300629846087925635441123675286788357345
9945300629670753108576348500644144388357345
9845294951288867325428734741710248932357345
9745252460828556043224118354404544980357345
9633897013632546841908592394825727247357345
9527798818896778243446298463375663343357345
9412919278968442120196310663279017636357244
933870511214316086778015888271450741347144
92236839120327120465353574415531624336842
9174176606393301843803684916774699326741
9058191932019890336483147020588672326741
8930899645028585883789312938179300326641
8829832089443891964762204321101088326641
8729500487160877915571949873474716326641
8610408955723143058255630938570900326640
851040459991860676554211499131122316339
84928085433328865976914189592554306339
83922247807023952096079498019250306339
82892444846579400868411972866558306339
81638228018280833672468328700837306339
8048666483671636354835231550936296137
7948662221161497564640062968696296137
787103022466726563098437477300285936
771536794541244623614925395429285735
76121583722740568273645446224275534
75121450672184882474489597696275534
7435182008390021076363643404265433
7317372552269360368533427728265333
7217369098972595585455801328265333
711020994496015397759874606255131
701020994160119368284769070255131
691002420668664158176457266255131
68554614586029708521730652245031
67554185559226910297576844245031
662476827427759667740058224528
652096532244434311471270224528
64212319152360914299199214327
6327584373079009300889204125
6225262465853032800967204125
6123166722366697502762204125
6020926037022213386752204125
5920916510485840386576204125
5819337874710482930612204125
5719337600565718137076204125
56378860371017195596183723
55342284137776516584183723
54341978130563929400183723
5397995995365713424173622
5297627162288019560173622
5195810973516749932173622
5049218128293009760173522
4917444458374391288173521
4817138747829520396173521
472783521300720846163320
46608310882180287153119
45599852455637939153119
44599825258665811153119
43512166253983233153119
4281041908142188143018
4127950430282103142918
4011610051837124142817
395817003372578132717
385816975658914132717
372947903946317132717
36333349186006122515
35232039258376122415
34232018753064122415
33231852949304122415
32201669082004122415
31201509576804122415
30200316968444122415
29200267707484122415
2828476193256112214
2753921200991912
26Prime!    7852695181711
257789407181711
2482714307159
2381287627159
2277236427159
2169277007159
2068771207159
1967316447159
182250646127
172210686127
161224206117
15877635117
14746475117
13349725106
12342165106
11910374
10644364
9560364
8203353
7160353
680243
528242
44121
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 3 and base 7
A259377

L equi 10

L base 3

L base 7

Next >10^40
1497426040455736833277049166191657584455648408448
1484814125322255788484018851584723559828324408447
1473950446641918978329429083490340918524321408347
146562839988544757143086167707462698346416398246
145479612322769751771290035621368787890920398246
14479696384314209288214808355751677026648388045
14360895895751175828228172735225045870836388045
14256021991587278934202956534959063211644388045
1416914524111793982447475129301134629136377844
1405071856555861661278669290778383961912377744
1391347062558818883606968743762957628508377643
1381023151565947065038676040993461180160377643
137996144397856120355913695145790473564367643
136960160354394559570936213526826032108367643
135202542517802318380461491592845449232367442
134140979403986737997166874558303950064367442
13360498008185585458104549917290276776357342
13228494072033532592872103609900265757357341
13116129411269653356858726580767823228357241
13015535122756870190975169819864361104357241
12912783253644156946310739823427082556357241
12812617661824841373874073235792605256357241
1273726742118366636819077237607170912347140
1262314144703136766320339868466242568347040
1252207432808008148895063279360852856347040
1241408953588062681315540872990861432347040
123915963580476282976682950639532296337040
122822578721566615001703440308658473336939
121627494297754298017382997899558664336939
120388804710544125891933512983903258336939
119204830010118034713654379475050756336839
11896063323405702524229074360085272326838
11780024210936050940332438258314032326738
11610455167211872589766263571512256326637
1158538423781299887209564756044338316537
1143828156743736467149216880722213316537
1133664801694981750325053583215629316537
1123259619353308680219542441994000316437
1111446970566101398217236850980168316436
1101444978125628902210544328253952316436
109342946905022314195630859239092306235
108307681079259407637824134716956306235
107266168831146417889941878259364306235
106141834412742234014192980634228306235
10584492178451293956724787212465296135
10432883692758210804331422160480296034
10332294028175738454804337734744296034
10225011550774950155124138161224296034
10114030649052851382158987629648295934
1007518940881527350060352720446285933
995836729815257199982854661054285933
982269940463516952351456409164285833
971444906092442977652509262718285733
961341872810590023265242655058285733
95295875117757891884117362920275632
94289708145913380867472049384275632
93186204729659325754555223200275632
92130320919751855769544582280275531
91109364142046079127449894992275531
9077149149093949161519687988265531
8950772645098774794742632052265431
8811899767742856504936509192265330
872939144234733141879192412255229
862272476265566123596598532255229
851629258710898659034459800255129
84736301183207717787147244245129
83644449513925853629058500245029
82553658983693788118137356245029
81400341897012900468065488245028
80378346857606056071274512245028
79343550873981934470383600245028
7837790674156897878083620234827
7724871504126683981647015234727
7620202287143923694819172234727
7519792663061377198446029234727
7414492914970724913820791234727
7312740373453026608614499234727
72979838454518061976304214425
71314121124263032247050214325
70175469998392732393832214324
6983996138774758424168204224
6874378389632102455888204224
6771005734774446229088204224
6624633761312367628301204123
6517263015931639807599204123
6411517148240701376184204023
631555316911250634016193922
62988421346024174056183822
61418138444696392656183721
60332251822186446404183721
59320754726799278860183721
58315307247753837405183721
57276769804176685816183721
56145103278493444048183621
5570150821079952416173620
5431966439598053368173520
5314959744316064584173420
5211207352411046784173419
516410639089100872163419
503959720840467478163319
493660645308508736163319
482921460800777086163319
471734195226323428163219
461560764115683240163218
45429162107575160153118
4445221839119556142917
4322666883572232142816
4221772277941544142816
4117136683996456142816
40830172165614122515
39469837033600122514
3868095147754112313
3765304259157112313
3611641189600112212
355642510512102112
344346524576102112
3318482764091810
328700161681710
31356649088169
30249193608169
29115028428159
2833165207148
2725854887148
267415866137
256397216137
245329006137
232339206127
221120486116
211080166116
20760245116
19540085106
1814762595
17Prime!    9103495
168200495
151312474
14400364
13328363
12242353
11164353
10142353
9121353
8100353
740242
616232
58122
44121
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 3 and base 8
A259381

L equi 10

L base 3

L base 8

Next >10^40
69162359278520900215856383685780539773625398143
682683038259170255102377896506684256834377741
6789466983784470480418231015346096852357439
6661574165797089552048768819677461370357339
6543241121232235223138747522208461634357339
6442753181234920874110656162125216450357339
6339016075779003777250286104143356473357339
622563314770425925222774429866924159347137
611545361050726990388858175005695028347037
601491818307380069720999298521748388347037
59761574857827605036004917572912018336937
58701779577426974646465095406098058336937
57569575077446777325583456120099889336937
5623910609634510060776103167339884326635
5521859999990562955759271043477204326635
5420782940150816165485329633068420326635
53Prime!    9154421879941826706077226079285931
526847668294130407868079804581285931
516614183335974819598448840533285931
505587862667455230409238810148285931
491300971894075676453696832705285731
48104733087250486270746962077275529
4762640237884220491248829899265529
461736119490786802694818797255127
4519696288940599156883084234725
4415638859489377858244307234725
43364695395569897227580214423
42360014620577548665916214423
41330300143900971857820214423
40304720541325476344844214323
39249655679139170920475214323
38249636212093446658075214323
37196406739090043790506214323
36195149355943974110314214323
35153561319370542367554214323
34150326844251484391042214323
33120014682355984031785214323
325741752257294068668194021
314949458745712184468194021
302999263443800192930193921
292959907850689099042193921
2879174156601271388173619
2773083110864755396173619
2644880998812567514173519
252127271328430823163317
24363376288168081153117
2321056462595764142815
22419572845958122513
2181473867465112313
2081452592329112313
195691134677102111
184099065139102111
17674709168179
16589614438179
15Prime!    15541737137
1412769167137
1311416527137
129440356137
1117492595
109490495
98578495
8316363
7203353
6130353
5121353
44121
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 3 and base 9
A259386

L equi 10

L base 3

L base 9


Please refer to the OEIS b-file at
https://oeis.org/A259386/b259386.txt
The list is too long to replicate here.

 

Index Nr

Simultaneous palindromic
in base 4 and base 5
A097929

L equi 10

L base 4

L base 5

Next >10^40
63989902758394082404439501467984583768238396556
62770260406344873604365351928091728852742396556
61701544395366111371801172108166795136962396556
6054932186713990109171882759006470320474386354
595286590569649576833344916297674236607376153
584966223874772811958947793284797920507376153
572784826315570427297069174398592373906376153
56319082004302898504154759899731456863365951
55283068338757232465154240263649576103365951
54135557948158440342149899593545201961365951
5316744408472524626488855453751056819355749
5213149871724927726140401624538567818355749
5111045197632469903559467887239174178355749
506247275049399443960845553691721841345749
49821591992463106132184516455026826335548
48691456520816410058182223440016674335547
47625924520876973172587187112529389335547
4623535338409060761284006963495329325345
452932697423081764249792764707862315144
44223840122933449651218067506974304942
43180542882135903252697201628998304942
42164081942492286523907940672018304942
4110522592351711791141971361826294741
40840845780587811390646946682274539
39374834541193166635043046001274539
3861084010310836230570914979264337
372646282288990142480241714254135
36217492970066095627136046243934
3512454588508239508448042233732
3412009763459975975060362233732
3311320022857296028412262233732
3211025274475869249136982233732
3165738451925934654491203329
3050248128332089611706203329
2949903539441293379706203329
2841186255976066325426203329
27Prime!    4390844685981744847193127
26Prime!    250855520885240759182925
25234602176132265223182925
245892002867556037162723
23383478037564629152521
2248517516968462142320
2147470618709562142320
2037004798195346142320
193101308506654132118
182806999337418132118
17155784877126121917
1616619231967111715
1516516113567111715
14Prime!    3231793381311
132565101781311
121740224181311
111709984181311
10259320671110
9234750671110
8193662698
776449597
69222476
546233
4Prime!    3111
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 4 and base 6
A259376

L equi 10

L base 4

L base 6

Next >10^40
1164278720928564228059585088913917719935075406651
1153433323632809892363652255312406458726730406651
114447771564640709495843832642332808305685396550
113127990230935372049374024491031514358025396449
11262317545014224243734999801825982337774386349
11162064501611954663666600449797970400174386349
11056059291028882300933223406247088393770386349
10925363552434268371326111705675297310001386349
1083102436780539144032161715828289243478376147
1073038334730951120707992412020559683974376147
1061169771735138316862254490999883342155376047
105119779602610887394086017203646599477365946
104109067277036831867133875591788253205365946
10387188342810855990414323028409690305355945
10246635555846738639920386858301726450355845
10117303743332979711532168726131450199355744
1002410155576375014613071514139695005345643
991867635467512717219892183743009845345643
98273590343090710902654959666907095335442
97245608768726579309421994132439875335442
9679931943689988905651066160426047325341
9560480099631409366916133100836798325341
9422504046897533455442004401357009325341
9316181697280264383187286569483315325241
924120217153404425095566272368647315140
911335638324365197370295761942977315139
901163974736788262126982861685995315039
89780120037554707778887399629430305039
8875797850684468208533520952095294838
8746418171845004945369773915990294837
8643030926448527690243993084130294837
8519671180416335368378701954239294737
849454288917455153272429366445284736
839449489361159738349359876269284736
821528105232425594681769918705284635
81998454579783805691500588467274535
80781581187910583794021042762274535
79515105795301240011595010729274535
78323965626852485400357158785274535
77282113709278044189332596075274434
76217597823403310886630768590274434
75202296763292733127123834330274434
7428905615700457082262133493264333
7315385077897761866694440675264233
723590031701062539850854590254132
711884698605883136111383497254132
701173132863151708769544495254031
69387701073737712289539205244031
68283921438192113318264079243931
67262939069637352216846007243931
6622385642689251517474785233829
65Prime!    6372205983137069544853223729
64727070725217607363190213527
63716609877969961732582213527
62284110399839401441695213427
61258942009983706473995213427
6024025722803574072773203325
5911550098019396133130203225
584452455483471325407193124
571179899868668886337193124
56636351200832860530183023
55523628978023895325183023
54509127549196054605183023
53434259874286090505183023
52127154149795232525182922
5180394116386707921172922
5072073074246336513172922
4910023898627083698172721
489998493962835122162721
47933118742276119152520
46550117934650493152519
45404400465825765152519
44403705181414373152519
43329536806222753152519
42323292550693473152519
4146164680151002142318
4030255762326713142318
3915822654274715142217
3812887266632430142217
3712761538567790142217
3611931403417210142217
352281658774290132116
341809863435625132116
33401478741365122015
32270747359295121915
31186398221946121915
30107074105033121915
2912982275395111713
289330794722101713
279233901154101713
264165108015101613
254036503055101613
243614009815101613
23Prime!    32250961791511
2223175589591411
2122389205591411
203334886181310
1954947257129
1833140837119
1718568457119
16196606697
15Prime!    69313597
1414539576
1312691576
12Prime!    7517475
117373475
101885465
9819354
8215343
755233
621232
5Prime!    5121
4Prime!    3111
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 4 and base 7
A259378

L equi 10

L base 4

L base 7

Next >10^40
873208335417623918881589225913802301351830406647
861930634892111749339055946970021674668965406647
85834105986086740570951451253087630396214396547
84779785196113126502338217877568464448134396547
8398783731441304499976688455660375917985386445
8282220656561921215526951299399808793055386345
8171016038223944683307593832890904026711386345
8064829883146416318566976637838033474755386345
7956972646383246025158373509395816943082386345
7837328739440340518177796342278873175309386345
77485425984681195633774157830352633205366043
76359488416905620428721990081961278545366043
7520499494904235578987007818283907647355741
7410384227571844686795237999694561277355741
73870331286866229899641376513071850335539
72859483964152746075625377250083434335539
71355381135697299622734425007625361335539
70353896939394028102683384517288785335539
69135474533133726096579796665874345335439
683121545992454685854367140046454315137
67321014843652281958838910064385305035
66217075683400180543380200924666304935
65163232869909980251059041593282304935
64103363713333260713300185120197304935
6389390244592391380553282968609294935
6273909036072425415300315613115294835
6169887316672175424501297268555294835
606623080511558364091888920149284733
591807856006417368403770842485284633
581224340447848565316937321599284533
5763995036322697967539289799264331
5647566482518578810820594038264331
5527587024291623263689560549264331
542638896559442399728684770254129
531432896717582234021128161254129
521176137521373269234724975254029
5125832614487515353354965233827
5013582685517334809482286233727
4910901860119248612490950233727
48926561758657919494947213525
47818394448405038406990213525
46203976863667466529550213425
4513773316835159709950203223
4412007980674606373530203223
436017746453312946885193223
424218808128230591659193123
41241521030849544855182921
40188077235829465306182921
39185569961319483162182921
3810556338547376278172719
3710490343658800214172719
366109256963409813162719
354467627704385132215
343628335729863132115
333304611554563132115
323205015384750132115
312047644601565132115
301871644872505132115
291134972961921132115
281103782149121132115
2730592589645111813
2622182595205111813
251692399385101611
2474249428691511
2364068074291511
2243042165791511
21Prime!    42462319391511
2038797368591511
19341794588139
18319466058139
1792624507129
167864356107
154285856107
14189806697
1314811575
1213655575
119958475
108802475
9Prime!    257353
8235343
7150343
685243
5Prime!    5121
4Prime!    3111
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 4 and base 8
A259382

L equi 10

L base 4

L base 8

 

Please refer to the OEIS b-file at
https://oeis.org/A259382/b259382.txt
The list is too long to replicate here.

Index Nr

Simultaneous palindromic
in base 4 and base 9
A259387

L equi 10

L base 4

L base 9

Next >10^40
1203986614795504905059420153771668699401710406642
1193646671246473011363623361580639803203050406642
1183084925217898081659365792974322951352390406642
1172928415125427305953640138689473719455330406642
1161282776835589345389390417326033258529103406541
115901863718819392901406583827528870852202396541
114688092165226463855984904202770624129346396541
113606245345428013083532891783531387834509396541
112279936793441903847108472941354891568775396441
111260700861476403301075736536582294358035396441
11011163458828997572197887126637878970770386239
1095468124769833361779661391852900140865376239
1082957382480359456459478665222176250290376139
107191465328388630467323034723727179206365937
106176443405556231714756188515514809298365937
105126163315526077740835764703326456905365937
10414282330701495367833817547845984270355736
10314282134294807878539452575550119950355736
10213559704872647456048645231189133530355736
1013832005129225582988648629820898110345636
1003537929036681994977031610721876410345636
99466976584346832623115925115184181335535
98225440926699707231019083773892430335434
97218250330992687482938317769664570335434
96192696746892900536580823099605030335434
9530028906961015280695024502195125325333
9425983856589222340363577577602885325333
939694514666361405013008354784685315233
929104807919429400264495462149005315233
916057694505156674148207286902065315233
904134934748542011663331628385031315133
894102020967094599596109273326835315133
884101826526605309267966646785267315133
872928407977495343253374422427590315132
862838107206662564480720905593330315132
85906180513579592880726935666910305032
84856043308186707804645299391290305032
83677978225921575966119869197090305032
82310541549338262431734389647279304931
81257750270834213101109411732487304931
80212495594888856871794342157034304931
79133167905449094603537172498153304931
7853862191128432116672621666490294831
7740226913247404020157470453570294830
763151829868840900467176542090284629
752064091907282510209449238185284629
74999054096418122759922345651274529
73966800361440575394034973651274529
72947170633179538258867238851274529
7142915627177216739984260978264327
7024859431735222632534180229264327
69656360463208623931490210244025
68512316862798137701645625244025
67268012995316802487587019243925
66179221801769704945267670243925
65132702855391552563697933243925
6449616465657989265220650233824
6344492924054937098124950233824
6212382332486929468617690233724
618681087085023693544029223723
608374485938206835981645223723
594622770904785005012655223623
584616614573521061351855223623
57750791439727272752010213522
56655054067808976740530213522
5597830227132597053205203421
5455327341317278801918203321
5353694063656991154606203321
5253526713487999458926203321
51Prime!    22346657910193902193203321
5011303748773839091510203220
4910552570503887949190203220
48287411961823187455182919
4716046526958346267172717
4612173822386241658172717
459888480378524210162717
444728069796793537162717
432172761848365805162617
422114967436733485162617
41743215116795690152516
40204973846313390152415
39198777976021790152415
3884470553495345142415
3738244097345762142315
3611372760382810142214
3511356994802010142214
349295288254930132214
332292918574418132113
321014966912315132013
31902465909895122013
30204283593150121912
29174913133450121912
28160142137430121912
276899910553101711
266852736153101711
252299011170101610
241634907909149
2399717507128
2242109457127
2130801747117
2030277587117
1925767587117
1818984457117
17Prime!    11817297117
1654215585
1523205585
14Prime!    16319575
132910464
122730464
112550464
10546353
9Prime!    373353
8273353
7255343
610222
5Prime!    5121
4Prime!    3111
3Prime!    2111
21111
10111
 

Index Nr

Simultaneous palindromic
in base 5 and base 6
A097930

L equi 10

L base 5

L base 6

Next >10^40
784810695707392702394862644463024525679163405751
774072599180405823588332740320964343487097405751
762649406874187621253659660274134899127321405751
751677801195489258147853281718168273134506405751
74106544937547160918622616541179378431196395549
7388430467812147691239774459505734306861385549
725453834802457998859241724262253469037375348
715269812829048163754248740900597708357375348
702820859858307829398346758004617190406375347
692587711359766685124492778252685301976375347
682480400444475586968450611206900924301375347
67286596641514377579064068478986619758365146
66135121780630713971334944064422590711365146
6514656642423758092455830024140398829354944
644032602737678277987586273236102701344944
63192153378359995782433125186516206334742
62150591321335972236202215784254651334742
6124859162446802554105945514958359324541
601013330642044861622728708365914314339
59434398577861530075154258456071304339
58396147319904980074931863342841304339
5739019197864006363147652957059294137
5629772912644532228304070934908294137
55Prime!    10610475356306916907729190101294137
5410541144816431211538366631201294137
531474435361059724946756814529283935
521287974239295403598689901588283935
51873156100954554823148296887273935
50527515174756306306562753911273935
4971043362050469832847769449263734
4832392039303998120303754132263733
4716492583864974596343645826263733
461029370576677268681190866253531
45979434010043797315416316243531
4477705358028106538715958233330
431011875381060617752551223127
42166139675801802801539212926
41132450774427686689338212926
406092831596205037679192725
394934883644169952933192725
384384942329377565347192724
37269196579469276814182523
36190645138816971853182523
35141417349010810857182523
34128031593329179827182522
339779924118261554162321
323099677168429681162320
31451853066660344152119
30275956595195822152119
294262839618051131917
28341225573632121715
27330347455102121715
26303520083621121715
25246467321391121715
24240971251611121715
23204185363456121715
22198522549056121715
2140232754191312
2029737900691311
1929597950691311
184861662481110
17883407698
16755846698
15723296698
14704396698
1327741576
1226691576
113074455
10Prime!    2293455
9651354
8104333
798233
6Prime!    67233
54111
4Prime!    3111
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 5 and base 7
A249156

L equi 10

L base 5

L base 7

Next >10^40
1514473759171355079285881233411716662515258405747
1503721608414624822503299554110827898219442405747
1492973195529300077359657339640288945393452405747
1482383966815691766116033204187509034011816405747
1471058197804870156016577505503989795420148405647
146414714311607996075038058209114184873936395646
145102390016999130649011721652496900482546395545
14488459433927810148755502400236610231861385545
14361187779264944459854884815046363639676385545
14241436117882755804099507221194772682718385445
14138968501117070777388269581712903261688385445
14018012636837260914771139795501194690266385445
1396804533932552717975339562537512378528375344
1385204919992342424895660676746878609832375344
1374045133285029432616650102974455870896375344
1363121364215975444368095655059805383136375344
1351821382446084092117593036689345380304375243
1341272694387420459235292083250351141672375243
133535185094012782134223855217721880006365243
13279125145915228261036077086164217664355042
13176004444366601851200792006595846784355042
13065207741843940873419843498296209168355042
12951273810835554458189201257472190072355042
12817641834648906356846538443801086374354941
12715751805411626645053973897737923014354941
12612362823315175392904095454098171788354941
12512301166534511251877970626752752788354941
12411777563242560373235522194430216808354941
1236746724148815193333316461953325946344941
1226700818533729280905971150827123821344941
1212385326667540629653412439456221208344840
120656560359527387257175481781085894334739
119393221844888445648876607812118242334739
118168540376636047871478438097754226334739
117139420408728235320760831714497324334639
11666995034122542916681439587036832324638
11516997633060909330537787173327372324537
1148296188847991056676153064204661314537
1136976656235846405282914590736006314537
1121132685164796352402752513086624314336
1111062387283724915891027651425544314336
110927451262215976909057453099904304336
109431704296267795648880207994696304336
108410397106635055948803094251896304336
107261756867104094289452119024826304335
10683148521346411673992902651646294235
10554509933711420328377242799976294235
10440800628848939333221843355064294134
10325292184552896021327940095992294134
10211723054436656431355451572056294134
1012423501954731116357686995206284033
1001674355105238476906904350644283933
991472560409894462888796811904283933
981289371409650922995655125463283933
971213323128501753504342133958283933
96976207359933100790935423192273932
95282689870636916431667614448273832
9497248837521263942906315956263831
9370429024967205161023249899263731
9242310156535073785505473572263731
9135167969675743460448147137263731
902423988091016575847870104253529
892394539449288117532766804253529
882321960082349719678424248253529
871530277910898567168799142253529
861453617113906454431731562253529
851256031294979348958308702253529
841066391919678134643984896253529
831047531737761472233043741253529
82431184915313742016296568243428
81191971143478439368681416243428
8091956582424491712914848233328
7961910549215322379497792233327
7840851647091858572666841233327
7739695632789437991162941233327
7637637504634853696144016233327
758362079157242442395616223226
743695400097492315843248223126
732409216715720544526112223126
721256193516603697424206223125
711191911601483144093656223125
70501421356545418476442213025
69486267340125277760142213025
68348557712481567649796213025
6797411522344257146392202924
6618273867034949670162202823
656139100437190687429192723
644854611133682563408192723
634074872026917237092192723
623473187009111400832192722
612421099236773866016192722
60238359847236631248182521
59110535513802830796182521
5855358830255457544172420
5732369820521361192172420
568491231634043863162319
558152267045954638162319
547858433687515933162319
536746177019008522162319
525784321085207262162319
514951212613811152162319
50850046505221616152218
49298887675308328152118
48179568939231946152117
4737465698385746142017
46Prime!    4359505255951131915
45364482389232121714
44147445356024121614
4365252488452111613
4228581869444111513
4117493894797111513
407721681656101512
394191009888101412
381692569856101411
371680662856101411
361621093206101411
3576405957891311
3466370619291311
3315969040891210
32392802548119
31Prime!    348533638119
30347137138119
29224120578119
28181082968119
27179686468119
261862744798
251823544798
241636104798
231473368798
221434168798
21769621697
20593836697
19537856697
18100056686
1727616576
1612654565
1510308565
141432454
13856354
12624344
11342343
10114333
978233
857233
724222
66121
54111
4Prime!    3111
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 5 and base 8
A259383

L equi 10

L base 5

L base 8

Next >10^40
1184338438084984344548548784567617174405078405744
1173309321817878572564103781566803244831732405744
116559465038492731415388167215442393374502395643
115526545478425776338340152759807156978446395643
114255981979319542933061259228857677142019395543
113216356970291969581839821472432527809698395543
11256179125902668419643077402628968804501385542
1113723080849496592997090112137131623666375341
1102830932740172041632895071279774544906375341
1091154579612265391524927184268602796862375240
1081016304152858667096019165940375050182375240
107158516228193639583575113770934162991365139
10698995243354098638221565508326338676355139
10556954929815198954197283038262561258355039
10417512378861941310889052884867668974354938
10311799584771478617624858697911340708354938
1021303427811674303419257616065507396344837
101691970779314652954139951658161674334737
100467389194949078225316947712881433334737
99114528413793498174580722250664754334636
9886971039275718732701963738632778324636
9711206410076507717304394001532746324535
963149343204321885312062520066492314434
953090778741727110833090893893692314434
94896446989033799914111331768473304334
93560187112411271956401691265287304333
92487938771528811220327544066702304333
91357595141569724257077487795236304333
90220260351765519944228321410674304233
8946438994059207347160682520876294232
8821100738434704355342831875082294132
878171005605901844408515835814284031
865211433500346198243270244172284031
853053223543895710223923768666284031
84648505255932708405862159116273930
83377649275591334678573433626273930
82322265722903275100867208514273830
8186653822285652854777240476263829
8025487382829812805699949841263729
792316228643359278894376623253527
782314030467732744126824623253527
771936348220773557932236958253527
761173840264933086345709627253527
751031476655591285803726491253527
7436480483178144959240111233325
7330057860118055959950806233325
7229877312337558868438806233325
7126847971366701468478701233325
7023000527446742697204724233225
6922603325019284993823924233225
684080781443784421164734223124
67515771636274389087742213023
66489739517365774724142213023
65483298841095537541862213023
64467299175833745311062213023
6375003753306379661377202923
6244026278992431183476202922
6123183943016281734178202822
606205436790382323229192721
596018014891186143629192721
584952676794849410708192721
574367927778916423347192721
563127137795707197802192721
55927609347442003678182620
54873874206536745222182620
53108722249102656646182519
5287070543138674036172519
5172229221342410756172519
5063919308246503651172519
4954018307498782714172419
4848200460817298154172419
4715215146816292406172418
4614586052232559006172418
4510610347035085164172318
448630118003254643162318
434179976145681841162318
421837422543645798162217
411167704597006412162217
40610409921031306152217
39325005646077513152117
3814952142559323141915
3711073162740322141915
368866678870082131915
355809320306961131915
341284108810066131814
331274936571666131814
32669367713609121714
31469606524278121713
30176616961826121713
29139853034114121613
2842360367356111612
277300948726101511
265067084204101411
255018349804101411
242459962002101411
2371606459791310
2262131921291310
2155136653291310
2025716140191310
19322854338119
1853598427108
17563786697
16228222686
15151596686
1418076575
1311898565
122709454
112268454
10438343
9186343
836232
718222
66121
54111
4Prime!    3111
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 5 and base 9
A259388

L equi 10

L base 5

L base 9

Next >10^40
761031380386418482076375727389282782601818405641
751009895679068762940909452287838924253018405641
74999843014909060277653082006357850803768395641
73953722338805362503464715832329267492388395641
72572073682174496756633612704158282408402395641
71489108693304843859701819181460277097616395641
7012209297823179517733144815774867629676385439
697815922846817965006136307946852265563375339
68100250109491561578276602915544553326365137
6773539835530453493100719997091117204355037
661789555577602281350635257466284312344835
65413445353827582758133504482317947334735
6418820327513289762054337511287308324533
63346289086126623052276582372586304331
62127176810382875796805687779992304231
611945569574489109337674727276284029
601253139356458664773321826288283929
5952650092749011789101832143263727
5839133487208707938900931442263727
5738033028802994716682305142263727
5632069597049486899733035632263727
5528219542855239030952110971263727
5426106167832287485762598116263727
5324389894698003872375601791263727
5214873229511792835500014626263727
51103741003135040627183914243325
5080878247205875106032413233325
496018052775013543104556223223
484269900239369675819239223123
474180822381716798634564223123
464158533008452431931664223123
453826106638174759948554223123
443364498607953856592018223123
433178469067542953830138223123
422419372800668579386862223123
412022907297133895992102223123
401813372452478843107346223123
3982763508198753336507202921
3842838465487714339826202921
37960588069334571508182619
36911840478745176528182619
35256320146951057809182519
346284871831461142162317
336221009414075142162317
325744620259340762162317
314287997640956241162317
30145464252692586152115
29137416991943786152115
2871088928149468142015
2770942565653068142015
2626358878059111511
2524863844904111511
2424208576998111511
2320134447808111511
2219671459008111511
2112607012902111511
201677684797
191412768797
181313858797
171142597797
1648553575
15Prime!    47653575
1441667575
1332152575
1222386575
11Prime!    701353
10564343
9282343
8246343
7Prime!    109333
66121
54111
4Prime!    3111
3Prime!    2111
21111
10111
 

Index Nr

Simultaneous palindromic
in base 6 and base 7
A097931

L equi 10

L base 6

L base 7

Next >10^40
774232896903459965201764021258165988534443405147
764050246256313450398087478161136872723637405147
752286831753589898561241721802625264005702405147
741331626584183044217840115203079443921391405147
731140466652112610962988746555165880454293405147
72866439809153647731786025798024937253409395147
7189957019538021669643985896059087389916384945
7057034395978995557677451952524718061704384945
6951228145189210616784880408390249422440384945
6846883109381761452353478247768909357414384945
672933456281647389965204005368182817512374744
661979883731524163780976989151876125121374743
651044675764046740936387366000013842449374743
6417670264882901145546510727122411665354541
631998557513159804128688198812227040344340
6214891147472823054524051494455297324137
6145986882914075623029164814920293734
6042262532385854248401647334808293734
5929366087957670669079239285728293734
5822614733959062086640523386384293734
5722382993872078653140615040776293734
5645260154647336774620537085263331
5537543593913872643173805264263331
5418188587189864622475158912263330
5317390284687668979110275648263330
5230595992552735111704086232927
5119524786585944179904793232927
50763935242386707102652212725
49668496304052005621965212725
48479871791497878191414212725
47255450059055825463705212725
4626089964728430283743202523
4524835713299768685971202523
4424339885317146470749202523
4310684777862880029708202523
4210324628539087401800202523
418908237172623238851192523
40418394899248730857182321
39411331566980657307182321
38373054804455006608182321
37223438058101993597182321
36163830160024067455182321
3510231408608585002172119
3410229280954883514172119
336875219172190387162119
326116904274791985162119
31126532386891655151917
3013267882222408141716
2912262956787888141716
284102350269485131715
27321015775216121514
26231773764784121514
25204191148800121514
24203509031168121514
239689802280101312
2216025880891110
214252232798
20279071677
19271721677
18269957677
17213970677
16206620677
15204856677
14186621677
13Prime!    7703455
126148455
115854455
10185333
9178333
8135333
792233
6Prime!    5111
54111
4Prime!    3111
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 6 and base 8
A259384

L equi 10

L base 6

L base 8

Next >10^40
1298445571266626706796149546310347045901537405245
128472099180656608465374713123503821726437395043
127121006406873922706414641221968101941465394943
12684347481557952597563715640987688999679384942
12583551423816451147216271469800907566519384942
1243028706529284507557600028299025697874374741
1232472060159671599556016402523681067505374741
1222213616325217695633013313430022052009374741
1212208068065619698081951432491434820777374741
120329630173083563330936704668239163321364640
11983180290910958386320165720946230276354539
11865508832381431525300828187011677259354539
11764834913836269597181956250242231747354539
11664691001872098915291971428956267971354539
11542341287613327599915339024776652418354539
1142563937469470781952190067724360319344337
1132046114843474940103747102651848918344337
1121719793755024451433231163099652821344337
1111718416889269023855675269153660565344337
110515828444716043325794635800570721334337
109429376116840690171769953607072529334237
108305772425713526660637377913697959334236
107296733290288865530211603426157335334236
10643379124939343799523332263298817324136
10542666123278340883486195265094849324136
10432929665226673927456162032978910324135
10331975819392491102760655271188694324135
10217703746788790959950345260484571324135
10117588497800570602403331999792987324135
10016737443430918295890689737983187324135
9916011215642888684557465462984843324135
981199853006872202787683959771769313934
971179218144906231995781609832945313934
96589343263074769715888399925535303933
95569039931480881303784826776271303933
9438667760427857725853362163323293732
9338578813063424105751979963515293732
926755530670288291114209019229283631
911944384092037331351587625249283631
90150544164151401064594661559273429
8963194207141387401314160723263429
8860978405623386535042649163263429
8728582546841502580305447321263329
862134614269532095973527815253227
85137423898080424816426027243026
84Prime!    36808172245371104292023232925
8336677571538112250298487232925
8236466655482550692828079232925
8136143642155465771474031232925
8036140547047832144555119232925
7934176829866721135211471232925
7818779868883630660225467232925
779131782647891247369465222925
76Prime!    6561870189686046211609222925
753295429454574941021541222824
74587636422553353669503212723
73537799059792585250455212723
72527746494866314721871212723
71470473355044455858206212723
70226800596470478658307212723
6915385536281457855657202522
6815292492682301599913202522
6715055878270585464361202522
666676995959002864309192521
656670196618287715509192521
646604592701475687341192521
634610858255198740475192421
624464556519216209395192421
611373896414642050313192421
601331874276783373897192421
59498683205468936027182320
58485893308196560339182320
5753493764633670074172219
5631629295131227185172219
5524642663243594193172219
5421316861847661257172119
5318474790776900161172119
5212165877883083869172118
5111951590146783957172118
5011716742258786637172118
492098982030706015162017
48926464106240659152017
47516268720555889151917
46401205063672537151917
45371039856325905151917
4455584258482529141816
4333004205249575141815
4224722285628901141815
41Prime!    15813860880803141715
4015804478291811141715
3911760498311914141715
384920262093249131715
371756866976011131614
36396619220597121513
35318743407660121513
34186431605610121513
33166787896538121513
32Prime!    116755331881121513
31116606986537121513
30108218625313121513
2988574916241111513
2880375377033111513
2743253138565111412
268094406311101311
254061216947101311
243292861699101311
233286138051101311
222115191225101211
211830945641101211
201420737297101211
191192047439119
18845722938119
17569390998109
16468236028109
151032507787
14567434687
13315721687
127409455
115001455
10203333
9178333
8154333
7Prime!    7121
6Prime!    5111
54111
4Prime!    3111
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 6 and base 9
A259389

L equi 10

L base 6

L base 9

Next >10^40
1191052113335092998732675184781386747584303405141
1181052094771780434653335584798929210026991405141
1171051806249603904506898552064999017861903405141
1161051805904579268137051245390801152474639405141
115746321228614026224257337317308575359931395041
114485500372467265270343181869937674446017395041
113485444884636422979488910826557640734305395041
112208825344029938058518538384146939570039395041
11148167853975377836034088265794052286510384940
11045822076349903582929517177374547527670384940
10945038341674503760618291680334207267050384940
10845028777579795079434225762840681474250384940
10710892325313064022341010326123309411144384839
1063006121656510170524268168495539225816374739
1051673294959513557193672685446956665810374738
10427587362959318280297697335096645735354537
1037491900952571474960302260116081360344436
1026058976891829086379355060175407910344436
1012107592431791930422601319438354924344335
1002098289909398937027633931396737896344335
992098096253631810804095509742529928344335
982097803437659944012079297714507352344335
972096808481018219584105108654373672344335
962091491995469748109574007854175712344335
951856834318800720547421736469375193344335
941680906289496578868145821174362275344335
931416236608856615586557112484702340344335
92507838724280665026993834750876429334335
91506805403622577786453036307484701334335
90490427830659223524558671061837985334335
8929359057896132958624042284176780324133
881689769332607268226815996573290313932
87953744801537897699350211583500303932
86308049094420100905276048170814303831
8543565342119288184560442257090293731
841516255841108525724472609667283529
831513363242447754036072046219283529
821513260427430022687001600427283529
81127063682402001493215053000273428
8024025539493510922424220707263327
7916513038784015040228040506263327
7816168640115431983722673286263327
7716146197562731023804485206263327
763940421331623951645796920253226
751058577818789819451457900253126
74951203226760792496857810243126
73932217968638756485618670243126
72327027168484938050043721243125
71211235119967642615158853243025
70157638881532059237895130243025
697543644464891026942855222923
68Prime!    7437875238052201437091222923
677435885773210370814275222923
667354522058620583641579222923
657227259089523459447399222923
645780855532128153703611222823
634179084457659358014292222823
624130016026286608162320222823
613607297935409205057181222823
602192489455003261354262222823
592192489226583967415062222823
582172730243702661200082222823
571672349967949028125555222823
561637103709482544478791222823
55841776858189016532710212722
54837963541719726071650212722
53Prime!    25237844535689857919202521
5220526982298523749494202521
51468242151115317501182319
50340926523717507544182319
49203861282386826791182319
48202186253210480911182319
47197907886640180179182319
4612414212677911183172117
4510915838736621332172117
4410841022411090800172117
4310796808110179352172117
4210790519823772232172117
4110674979690311068172117
4010666075534207052172117
391658410356393350162016
3827832011695551141815
377264479038060131714
36327925630018121513
35187195815770121512
34185794441250121512
33184314116750121512
3255854298990111412
311244432909119
301240918229119
291234276229119
28694325178119
27Prime!    612817938119
26483079248109
257971580798
242515513797
232494129797
222488945797
212439445797
202350165797
192300665797
18Prime!    2295481797
1716814565
1616562565
158281465
145740454
133740454
12910344
11209333
10Prime!    191333
9154333
880232
7Prime!    7121
6Prime!    5111
54111
4Prime!    3111
3Prime!    2111
21111
10111
 

Index Nr

Simultaneous palindromic
in base 7 and base 8
A099145

L equi 10

L base 7

L base 8

Next >10^40
934086855796436419179002660753244019442694404744
923199476229410331299009380849084589707052404744
912689168004551284453907744967262345826107404744
902028409603411505745535234592301525601374341
891486275208312934121777245199373941185374341
88648530994100166015550413951201590395364340
8740842657715529378521786049605889401354139
8639852538295641271639689504332594361354139
8519689148945741767818515574752802151354138
84543790573416191001535609537458921333937
83490889469049967939691671294819361333937
82135526843321357943935723141254483333936
8116370275824486438409467182676363323735
8016312405579579711939011706363723323735
7912824195719312299063902475222114323735
78343438503379328618777313621844303533
77340906586281163116956219705044303533
76211712828510339489315395539178303533
75173686161749418552722815005962303533
74139739980143413644926503718449303533
73121604813280764952577989370529303533
727664176963242427973890138894283331
71Prime!    6932388311196319245781243813283331
706306384292335194578074214789283331
695552842733733915133970956764283331
684634340524657241477712108011283331
672719274933652545504342530314283331
661554946556600221066865116689283331
651274647020018484128813260353283331
64138010613055711059084806671273129
63130059210876440825105503662273129
62119559947638620192865474766273129
6172316738170897739901736427263129
6051129357539864572521886314263129
5945054935583868733070983506263129
5823471700433184433516915529263129
571692318257217276675683749252927
561609516373195632479853845252927
551591080944968905951591957252927
54776281129926615333209890242927
53773606944374822605769954242927
52767896597981600379300002242927
5121028571070154722639644232725
5015742604914850506892627232725
4911430221956147759328922232725
48543174425539340174295212523
47432746793552539117045212523
46423479048759927584237212523
45353873672982519332532212523
44299136638137274062532212523
43290293502938358099195212523
42277786634125993659955212523
4110688365729164780171918
406641481107049786161918
396622944330543930161918
386615812399178042161918
3768995850733945141716
364712469842177131515
353741580511478131514
3455027793502111312
3354464523606111312
3254453459798111312
311709813601101111
301556085529101111
2963083242891110
2827924649899
2710453500898
26786435677
25626778677
24502457677
23450985677
22447849677
21Prime!    444713677
20431721677
19428585677
1816708555
1713459555
1610658555
157801455
146953455
132997454
12300333
11292333
10235333
9178333
8121333
76111
6Prime!    5111
54111
4Prime!    3111
3Prime!    2111
21111
10111

Index Nr

Simultaneous palindromic
in base 7 and base 9
A259390

L equi 10

L base 7

L base 9

Next >10^40
1494908860193492460996518486383286641045940404742
1483307978228258948648725533043034809134330404742
1472808470157144577567784123101458727184120404742
146941959263065815287787895985458011121034394741
145359652919760286549623650245126841208480394641
14414514798318561028935116235007587279952384439
14312837063609273996685366749979559813248384439
1425679002318902254630532753630628704752374439
1411226391308235305826470154991754102940374338
140337345868784374988147965455743051550364338
139188146097102561240655808118578560680364237
13854236579291536383702427005915464432354237
13730014261976450087256556014420388806354137
13614539489993399946588211820589162960354136
1355769960441485554417880080053188480344036
134890755865300581144066324604652393333935
133674705682080674863417935143116464333935
132507355686200370963511712248134535333935
131202392614605747485985754892706140333934
13082127725184083239604912302081920323834
12919571135509749323237816669488808323833
12818590403256193395886543930719256323833
12714095051931520526645260979276864323733
1268610708981295661970446456009105313733
1258485427379895371445400448301388313733
1248339234751578352454132747565702313733
1235539936052668974793230591009703313733
1225060391802040612284787762374699313733
1212875192295457759077751700241500313732
1201608089992043068591870006543360313632
119387175575406995959706292929760303632
118368021811867878411318927613761303531
117279943711425248093482540156629303531
116261433037000838499933590963618303531
115257705201158166898411831578040303531
114170953031400893974935166933759303531
113123413579154059368077612835121303531
11282935828967850968849031431126293531
11143707376624437644649803607592293431
11041426184222597075506581698440293430
10939848625675907011918412780040293430
10827214311017969041744720493960293430
1075721838755307007179215318850283330
1064914741143220254562813792850283330
1054425074642154021149132861768283329
104195089372162579264517015240273228
103101413912165664911756048270273128
10256610533075239750846784246263127
10153769215474699117432355962263127
10030329725142933080567150477263127
9921043968508276327106413248263027
9810386484431147622299992752263027
979093795028805821118788432253027
965430018859347320428141960253026
952248040982182921844543300252926
942202075122626280493933240252926
93689454128054325863868101242925
92270328613129899251820176242825
9129004727469187267108930232724
9013859262950610032838100232724
899486441988338842652700222724
883729867203029045310472222623
873210760537386908728728222623
86854993738873524179850212522
85512072044301517020050212522
8492520418698791396512202421
8347987409188845232688202421
8218419097769705052893202321
8112346857701296110730202321
806704825946724092370192320
793507460573508033960192220
782945908644901976360192220
772767723069416266000192220
761153224512261940400192219
75993715719098312400182219
74568376956845068736182219
73511220556702236100182119
72432621948882842255182119
71282488203379766646182119
70208201514372069311182119
69165908503654004197182119
6863100241427288000172018
6711132375103763458171917
6610368492428697080171917
659812330223915785161917
649350709125459378161917
636221745601065984161917
621993926853603000161917
611104575959129640161816
60834424022498440151816
59811740650692800151816
58734723345582040151816
57206576333227900151716
56172921319185669151715
55147993832352958151715
5468503313361800141715
5320268849562000141614
522088800185930131513
511202029647736131513
50796259955485121513
4984668107250111312
4883714515310111312
4730862471355111311
4622668403353111311
45Prime!    20537111057111311
4420404027400111311
4315127811455111311
4213575144288111211
412225211080101210
401684866370101110
391940624329109
3822674550898
3712990350898
364084000787
353501600787
343344352787
332913368787
322756120787
31738100677
30555013677
29532900677
28400200676
27201720676
26164900676
2545600565
2422800565
2314762555
2214510555
2110252555
208200455
193550454
182000444
17400343
16328333
15300333
14264333
13200333
12164333
11100333
1050232
940222
88121
76111
6Prime!    5111
54111
4Prime!    3111
3Prime!    2111
21111
10111
 

Index Nr

Simultaneous palindromic
in base 8 and base 9
A099146

L equi 10

L base 8

L base 9

Next >10^40
117Prime!    677319371542831119686740547295441238399394341
116567431812242393858954316322742170488494394341
115481783860128563511702053883377791817389394341
114438578831595782400592115363168121736781394341
113326932641929528722974994724813287251827394341
112318927431840270574607919113245496917995394341
111182963020672513760446684008684268886602394341
1106430011706829691002509307448402143604374139
1096364368282399177595074699843226744500374139
1084982161189721646910675646136968646635374139
1072087658215071221020957428791599438113374139
106163642843502727665569018376517256255363937
105133471879514252145700758727716414686363937
104132195444131494196197309162550978006363937
103119024527058369278439096078587501997363937
10298840418013885943489517020660582452353937
10189254900750622115249443361965056212353937
10079956862061063119118520837213685683353937
9925812613744511672780560012518009289353937
982246735347178120016161371144802558343735
971927593352523125333957291261989693343735
961716246811792839559660394171885205343735
951168680450805051473456898365417379343735
94464819097914392038792637055445721333735
9329830703204991176538374722558013323533
9216673296450437284279626648405651323533
9115684371941308821653486909185859323533
9011124603068524800127856694896394323533
8910817072391914734560918568933386323533
888340823907573090829706193441897313533
877457949791252817803405789070233313533
86369747635817844286311056423596303331
85364294428150261037390454199716303331
84288296107972346602938967133739303331
83269293628521408879205766441051303331
82268040070906315593576900794395303331
81164943406543200202235850879810303331
80158994829277290897718539400706303331
79145881090966894475589584149873303331
78134641558278761413361882041641303331
778193895472684026254760966630283130
763043620443673103988244211034283129
751478275878038137213514200841283129
74125452061888235904224612830272928
7354582195927049631887321394262927
7249178422446718203844352674262927
7137069907546950614090717881262927
7033451634879190616085543849262927
6929270429666602161688112161262927
6826091811574308074986722705262927
6723087960070137799337056009262927
6622035618945659106995252745262927
6521737980790917961440346049262927
641350825568132355071685020252726
631324505431560669649823260252726
62844323158002595391777970242726
61624235205670475482510082242725
60303400467159904522039809242725
5929981800268742152705430232524
5822086503094014919558380232524
5721408139061976817599140232524
5618900858569591286370820232524
557579933953333805083553222523
54512918878693453369150212322
53359804954513570058300212322
52326364387585946501340212322
51215424957893108952250212322
50206181182637627497650212322
495111391307202132700192120
481205520295345991297192119
47120168724989001390181918
4681877825421774500171918
452229560302980799161717
441939137135947326161717
431767662936108630161716
421366179755723700161716
4133181029690535141515
4031285221426631141515
3919404342621340141514
38485724124423121313
37422454576718121313
36318713056300121313
355170508596101111
3498383349899
3371877268899
3263367795899
312067519777
301405397777
291373645777
28Prime!    1368461777
271294652777
261273268777
251268084777
241262900777
231257716777
22926371677
21899803677
20894619677
19889435677
1827310555
1717876555
16Prime!    12547555
1511314555
14455333
13446333
12Prime!    373333
11300333
10Prime!    227333
9154333
8Prime!    7111
76111
6Prime!    5111
54111
4Prime!    3111
3Prime!    2111
21111
10111


led Base 3 and base 9 led

You all probably noticed that I 'restrict' myself searching for large palindromes mainly in the decimal numbersystem.
Not so for Kevin Brown ! Here are a few palindromic tetrahedrals that he discovered in other base representations.



formula = (k-1)(k)(k+1)/6
kin base 3in base 9
100
211
3114
410111
520222
72002 
13111111444
14 555
15202202 
40112121211 
121 488884
393201000222000102 
4971102111111112011 
589 71066017
1094 505555505
 88574  505055555550505






Contributions

Kevin Brown informed me that he has more info about tetrahedral palindromes in other base representations.
Link to his article :
point On General Palindromic Numbers thumb up




Richard Gosiorovsky (email)
Dual-base Palindromes
[ do 2/5/2024 6:02 ]


Hi Patrick,

I am sending you in the attachment several
new records for dual-base palindromes:

base 2 & 5:   18 new records → From [26] to [43]
base 2 & 7:   14 new records → From [32] to [45]
base 3 & 4:    8 new records → From [28] to [35]
base 3 & 5:    6 new records → From [40] to [45]
base 3 & 7:   15 new records → From [73] to [87]
base 4 & 5:   10 new records → From [27] to [36]
base 4 & 7:    9 new records → From [49] to [57]
base 5 & 7:   13 new records → From [73] to [85]

Thank you for this interesting entertainment.

Richard



Richard Jones
Dual-base Palindromes (binary & ternary)
[ do 2/07/2026, 20:48 ]


Also I have verified that for binary/ternary there are no solutions at T = 93, 95, 97, 99 ---
so the next solution is greater than 3^100.

Regards,

Richard



Richard Jones
Ternary/Binary
[ vr 24/07/2026, 18:50 ]


I am currently running a 6 day run for T=103 for the ternary/binary --- if it doesn't find one I am left empty
because T=105 would be a 3.5 week run -- again unfeasible.

So unless a generous supercomputer facility decides they want to do dual palindromes that's going to be the end
of things - certainly from my end.

Regards,

Richard



Richard Jones
Ternary/Binary dual palindromes
[ do 30/07/2026, 8:06 ]


Hi Patrick,

My 575863 seconds (6.665 days) run of T=103 turned up no new palindrome.

All I can say is that the next one is greater than 3^104

I started T=105 just to get early timing and this indicates it is a 13.7 day run --- I cannot afford that time.
Since I would bet I am the only person in the world currently running such a search (ternary/binary) it will have
to wait until I get much better hardware or someone else takes this obscure area up.

Regards,

Richard



Richard Jones
WOW - after more than a decade since the last one -- I found a new ternary/binary one
[ vr 31/07/2026, 8:19 ]


Hi Patrick,

I wasn't going to run T=105 --- but I did start it going to just get an estimate of the time (I mentioned this in last
email) -- anyway I left it running when I went to bed -- nothing showing -- but this morning I took a shower and came
back to the computer to stop it running and there it was --- (50 decimal digits, 105 ternary digits, 167 bits)

93814833782752683486286194707262031368542962943489

That is a verified dual ternary/binary palindrome.

All I can say is the next one is greater than that one.

Regards,

Richard



Richard Jones
yet another ternary/binary
[ di 04/08/2026, 21:06 ]


Hi Patrick,

I sped my code up by a factor of 90 or so -- so I have been running some more T values. So my T=105 run
(T values are the base 3 lengths) which took almost 7 days now takes only 2 hours.

The next one is 42468857786616486687891165709191634653913393785544903

which has 111 trits, 175 bits and 53 decimal digits.

The next one is greater than 2^178 (that is a two not a three) because only odd trit lengths and odd bit
lengths can be dual palindromes.

Regards,

Richard



Richard Jones
Re: yet another ternary/binary
[ wo 05/08/2026, 8:48 ]


Hi Patrick,

There is no reason to expect an end -- the likelihood (very strong likelihood) is that all these dual
palindrome between two bases are infinite sets but with the density asymptoting to zero.

Basically to improve the speed I went back to some ideas in the past ---

The old code walked a pruned tree against one big precomputed basket, so its cost grew like
3^(h−21) — the basket size was capped by memory. The new code splits both halves in two and
joins them on a k-bit key, bucketed so each side generates its part of a bucket by a residue lookup
and neither is ever held whole; cost drops to ~3^(h/2). Then most of the remaining gain came from
tuning the four-way split so the frequently-read arrays fit in cache.

- packed 32-bit hash slot (was 4-byte claim + 8-byte key in two arrays)
- windowed prefilter — replaced a 20-iteration `ubit()` loop with two shifts,
a mask and a reversal. Equivalent by construction: bits k..k+pf must equal the
reverse of bits L−pf−k..L−k−1.
- **exact bucket occupancy by FFT** — a bucket's size is a cyclic convolution of
the b1-residue histogram with the B2 class sizes. One FFT pair gives the exact
max in milliseconds, replacing a bound that ran ~4× high and inflated both the
scratch buffers and the hash table. Verified against brute force.
- **`W = 2.62` in the d formula** — B-side operations cost ~2.6× A-side ones
(three scattered reads vs one), so `d = (h + log_3(4W))/2`, not `(h+1.26)/2`.
- **direct-to-buffer list generation** — blocks are built by a two-pass odometer
straight into GPU buffers, already residue-sorted, with no `Vec` at any point.
Verified: the odometer reproduces the old `block()` exactly, and the whole
builder reproduces `bucket_sort(block())` exactly (values, offsets, keys,
min/max).

Eshed and my code for decimal/binary are basically equivalent at the moment -- we both need a
week or so for D=61 and D=62 -- I decided to concentrate on the tern/bin since 7 day runs are not
feasible for me. I do have a couple of ideas related to my new tern/bin
code that should transfer over -- though it won't be a 90x improvement -- but I would think D=63
and D=64 would be feasible (maybe).

I've only ever looked at dec/bin, dec/tern and tern/bin --- you could go bonkers on these things
picking new base combinations. I just looked at the six/bin list and I see the largest is only D=20
digits --- I would think getting that to D=45 or D=50 wouldn't be too difficult
though with Pari/GP it would be - these codes really need dedicated Rust or C -- and if you stay
CPU bound with Rust using Rayon -- or use the GPUs with Metal (on a Mac) --- my route is GPU
with Metal.

I haven't used AI on these codes though on my regular work codes I have -- they do tend to be too
sycophantic at times and tell you what you want to hear versus what is true -- especially Gemini
and CoPilot. Claude is better but can still
fall into that trap. But they have their uses -- I have a code I use for work that went from 34
minutes for one thing to be processed and now it does over 1000 per second and I couldn't have
done that without AI - though I did hand hold it a lot through the development.

Anyway -- as to tern/bin and the new T=111 I gave you --- I am running T=113 as I type -- take
another 2 days to finish --- I can right now do T=115 and T=117 though again I am looking at 9 to
12 days each. So unless I have another breakthrough I won't run them.
And breakthroughs are looking less likely -- I don't have any old ideas floating around I want to try
so the brain has dried up.

Regards,

Richard



Richard Jones
senary/binary dual palindromes
[ ma 10/08/2026, 14:00 ]


Hi Patrick,

Here is a list up to S=72 (base 6 lengths) -- counting 0 and 1 there are 190 solutions.

{0, 1, 3, 5, 7, 21, 129, 427, 693, 819, 3999, 4257, 4593, 28539,
…
…
63477682887119514754025963222293559401531294573597095333};

All told that took 17 minutes of computation time. The code is quite fast.

Regards,

Richard



Richard Jones
senary/binary dual palindromes
[ wo 12/08/2026, 7:52 ]


Hi Patrick,

I have some more for you --- these took a few hours to generate -- Once you get past S=72
(the list I gave you was to S=72 - then they get more difficult to compute)

So this list is from S=73 to the last entry being the single solution at S=80 (which is 63 decimal digits).

{327403474216185482769927024752972089618377556771299403179,
…
…
152942926969395350568523312249103059155621059264974505326828157};

No more primes in there -- of course the odds of getting a prime is falling rapidly as the digit length increases.

I am continuing the ternary/binary case -- he is a new solution at T=113 (676710174766987245264188686637424310057228994099521607)
- T=115 is empty so the next solution is greater than 2^184.

I can do T=117 and T=119 when I find the time -- after that seems unlikely to be feasible but I've said that before LOL

I am actually going back to decimal/binary --- I just wrote a new code to do that (my current code is based upon Eshed's
original -- the new one is based on my other codes but I have yet to even test it)
but I have hopes it might get to D=66 (but don't hold me to that).

Did Eshed ever run D=62? He didn't bother with D=60 because I had done it -- and I left D=61 to him - which he did -
but I haven't heard from him if he did the 8 day run for D=62.

Regards,

Richard



Richard Jones
Re: senary/binary dual palindromes
[ wo 12/08/2026, 8:21 ]


Something you asked before --- my code won't accept any 2 bases -- in theory yes I could do that
but it there are intricacies each time that would make it a pointless and awkward exercise to make
the code generic -- easier to keep each code separate.

As to quinary/binary --- probably not -- as I said in a prior email you can go bonkers with the base
combinations. Enough to drive you crazy --- in principle I can probably do any pair of bases to
a decent level -- but it is not a trivial exercise most of the time. And there are only so many
hours in the day so to speak.

Regards,

Richard



Richard Jones
ternary/binary
[ wo 19/08/2026, 23:11 ]


Hi Patrick,

…
…

I still have T=117 and T=119 to do on ternary/binary -- anything beyond that is unlikely.

As I come to the end of these palindrome searches I hope I have been of some help -- it's fun trying to push a laptop
as far as I think is possible on brute force number crunching.

Regards,

Richard



Richard Jones
Quinary/binary dual palindromes, just for fun
[ do 20/08/2026, 13:06 ]


Submitted entries [44] up to [62] for the quinary/binary case.
Hi Patrick,
…
…
those are the quinary/binary solutions up to and including Q=57 base 5 digits. No new primes though.

I was bored last night so I thought I'd quickly code it. Those took about 12 minutes to generate.
Of course I can push this much further with a code tweak or two.

Regards,

Richard



Richard Jones
Quinary/binary dual palindromes, Re: just for fun
[ vr 26/08/2026, 8:26 ]


Submitted entries [63] up to [72] for the quinary/binary case.
Hi Patrick,

Some more:
…
…

Note that 1786401433715617032468486764257011989770277 is the first prime in the list
since the number 31.

Regards,

Richard



Richard Jones
and to finish off quinary/binary
[ vr 26/08/2026, 8:26 ]


Submitted entries [73] up to [78] for the quinary/binary case.
Hi Patrick,

I thought I'd take the quinary/binary case to Q=75 -- I had left it before at Q=67.

So we have:

Q=69: 3 solutions
Q=71: empty
Q=73: 1 solution
Q=75: 2 solutions

Regards,

Richard



Richard Jones
septenary/binary
[ vr 28/08/2026, 11:12 ]


Submitted missing entries [33] up to [35] for the septenary/binary case.
Submitted new entries [49] up to [74] for the septenary/binary case.
Hi Patrick,

Your list for septenary/binary was missing 3 solutions at S=23.

Here is the complete list up to and including S=51 (S=53 is empty by the way).
…
…

Note that there is a new large prime --- here is a list of all the primes:

{3, 5, 107, 257, 1566399158893, 2059577471782805986901831467}

Regards,

Richard



Richard Jones
and septenary/binary up thru S=61
[ zo 30/08/2026, 15:22 ]


Submitted new entries [75] up to [91] for the septenary/binary case.
Hi Patrick,

Here is the continuation of septenary/binary from S=53 thru S=61 to go with the list up
to S=51 I gave a couple of days ago.
…
…

Regards,

Richard



Richard Jones
more for fun in base 9
[ di 1/09/2026, 19:41 ]


Submitted new entries [70] up to [97] for the nonary/binary case.
Hi Patrick,

Extending the nonary/binary list:

nonaryBinary new ones:
…
…

Note that 2073722573406568398837217962245683 is a prime.

Regards,

Richard



Richard Jones
page 3 bases with(out) binary ones
[ vr 11/09/2026, 9:49 ]


Hi Patrick,

Here is the data for page 3 bases excluding the binary ones since they all already go to much greater depths
than 40 decimal digit levels. I am also excluding cases like (3,9) -- any base where the two bases are a perfect
power of a prime has too many solutions - and you already direct to the OEIS b files for such things.

So I am attaching (3,4)(3,5)(3,6)(3,7)(3,8) (4,5)(4,6)(4,7)(4,9) (5,6)(5,7)(5,8)(5,9)
(6,7)(6,8)(6,9) (7,8)(7,9) and (8,9).

The primes in each list are:
…
…

Regards,

Richard










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