Palindromic Numbers other than Base 10

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Introduction

Palindromic numbers are numbers which read the same from

left to right (forwards) as from the right to left (backwards)

Here are a few random examples : 7, 3113, 44611644

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

Simultaneous palindromic in two bases

Index Nr	Simultaneous palindromic in base 2 and base 3 A060792	L equi 10	L base 2	L base 3
	Next > 2^178			T
19	42468857786616486687891165709191634653913393785544903	53	175	111
18	93814833782752683486286194707262031368542962943489	50	167	105
17	24014998963383302600955162866787153652444049	44	145	91
16	32345684491703244980406880704479906642045	41	135	85
15	30412638162199251273509758127730300026189	41	135	85
14	1597863243206403857787246920544522912361	40	131	83
13	428027336071597254024922793107218595973	39	129	81
12	32456836304775204439912231201966254787	38	125	79
11	392629621582222667733213907054116073	36	119	75
10	8022581057533823761829436662099	31	103	65
9	2004595370006815987563563	25	81	51
8	1922624336133018996235	22	71	45
7	381920985378904469	18	59	37
6	90396755477	11	37	23
5	5415589	7	23	15
4	1422773	7	21	13
3	6643	4	13	9
2	1	1	1	1
1	0	1	1	1

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

43	34083641094041215425827207	26	85	37
42	30101157511305300778061027	26	85	37
41	20563671288597289812895761	26	85	37
40	105531909578180191904589	24	77	33
39	27166507811241546115101	23	75	33
38	2792665749769510987497	22	72	31
37	2536733867455442723217	22	72	31
36	2449913965194573706017	22	72	31
35	1999022506621150444827	22	71	31
34	1849130200000590372371	22	71	31
33	150319808235063576129	21	68	29
32	136329883505815551543	21	67	29
31	122932536640098304683	21	67	29
30	120110524940556687883	21	67	29
29	89701695563295218137	20	67	29
28	73819093863158149121	20	67	29
27	57338685589431482211	20	66	29
26	1705198171059456701	19	61	27
25	267590170057856439	18	58	25
24	202124162283446733	18	58	25
23	151875068667242337	18	58	25
22	99805500812710541	17	57	25
21	8829547069230943	16	53	23
20	6299497017331917	16	53	23
19	4738749440161121	16	53	23
18	2996750083037781	16	52	23
17	286118927218753	15	49	21
16	567897922593	12	40	17
15	169179279801	12	38	17
14	26777829859	11	35	15
13	17935304097	11	35	15
12	7609865031	10	33	15
11	340134981	9	29	13
10	682341	6	20	9
9	520831	6	19	9
8	38937	5	16	7
7	2709	4	12	5
6	119	3	7	3
5	93	2	7	3
4	Prime! 31	2	5	3
3	Prime! 3	1	2	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 2 and base 6 A182233	L equi 10	L base 2	L base 6
	Next > [190] Table under construction.
144	170733988420915786250229139189095234239327	42	137	53
143	95855098376365535490955547822226543024945	41	137	53
142	35212062210638853808471338737178179841907	41	135	53
141	32196226188076909627097854231542543342781	41	135	53
140	18417536835574991246349957988197217795611	41	134	52
139	15880954831118203618731674396561089000797	41	134	52
138	9350607661169712922344337972595483159515	40	133	52
137	3207240676705813056105887178900398912361	40	132	51
136	2906716512288108363692005540751561340177	40	132	51
135	2465297165358307435013759482564104137703	40	131	51
134	Prime! 133957498046208178608172058508570751379	39	127	49
133	112767926771820416256296577273644266901	39	127	49
132	84723795130247090801171557978439626623	38	126	49
131	14706845490752154862791314990194188429	38	124	48
130	6819601526227334927632344411068740645	37	123	48
129	622167395013529005140638833593705975	36	119	46
128	369484894697302697271054957214190193	36	119	46
127	119879344479442718793063432664395037	36	117	46
126	107913983583749011489923894246187621	36	117	46
125	61949304328059089213243753964676989	35	116	45
124	55489443080404023181547246160101205	35	116	45
123	33652462524004883960723652560578291	35	115	45
122	29728551639811822976803614595935469	35	115	45
121	29545337654645056634130328814512237	35	115	45
120	23839259120491206010309087741204297	35	115	45
119	1739743732489528623000224571503061	34	111	43
118	279008562840154830234915860813883	33	108	42
117	249636853569637276958009011189539	33	108	42
116	126175341184186806916005013194979	33	107	42
115	126146738873604287377128674189539	33	107	42
114	112726282006184003334695092984717	33	107	42
113	81187169510578567961709247260673	32	107	42
112	53392678384727045991390907620885	32	106	41
111	43230065676024338748941384226321	32	106	41
110	23098221660921938430582575637385	32	105	41
109	2188215397516195388209434210107	31	101	39
108	1924003540322510229911395525187	31	101	39
107	1246309779233513025508473638367	31	100	39
106	1151460991958764761721321328919	31	100	39
105	594057412834676046160977203191	30	99	39
104	590250036124062960060569380471	30	99	39
103	Prime! 493729853550986902109639562979	30	99	39
102	335090923209477962166023351009	30	99	38
101	1071558545897407097590245819	28	90	35
100	1001420152774788863902968051	28	90	35
99	Prime! 540770568795997877440747003	27	89	35
98	416236030633502957919626293	27	89	35
97	400653544480402135930580389	27	89	35
96	398732494354320733571553061	27	89	35
95	185917164959453833657750425	27	88	34
94	171662799836802452809646001	27	88	34
93	156780573668704785535726977	27	88	34
92	9357001767213361375852015	25	83	33
91	802965820999708024967253	24	80	31
90	704230003987273379873961	24	80	31
89	316606603738187666909281	24	79	31
88	Prime! 34579344526412674075223	23	75	29
87	33783643594880314423079	23	75	29
86	24207503363570422943781	23	75	29
85	22419218190317444716521	23	75	29
84	7840845872292061995307	22	73	29
83	7503607230677085144787	22	73	29
82	6666318737698860764461	22	73	29
81	3574872687181455610755	22	72	28
80	1407478774388559878425	22	71	28
79	570868485923851782639	21	69	27
78	529106159925017013927	21	69	27
77	514888825293028733691	21	69	27
76	307741857092771540641	21	69	27
75	297229306823447209729	21	69	27
74	17836907961939038703	20	64	25
73	14606792210184908115	20	64	25
72	Prime! 9027418797989294431	19	63	25
71	6851803640999392381	19	63	25
70	442782624909444387	18	59	23
69	421678237970776797	18	59	23
68	66914369589632439	17	56	22
67	35031040848860959	17	55	22
66	25318737011894221	17	55	22
65	24109374625379029	17	55	22
64	13294033268299581	17	54	21
63	12825774359298669	17	54	21
62	12141647369392437	17	54	21
61	11931182927622549	17	54	21
60	6636395485755709	16	53	21
59	6451588843354861	16	53	21
58	5214602113362985	16	53	21
57	4978544622304945	16	53	21
56	2040316732420071	16	51	20
55	535608924080591	15	49	19
54	Prime! 129956651976247	15	47	19
53	125823357614887	15	47	19
52	121593745290427	15	47	19
51	105026120405245	15	47	19
50	62995659142311	14	46	18
49	59238470140395	14	46	18
48	27303621891427	14	45	18
47	11214404390085	14	44	17
46	10982103577593	14	44	17
45	9154514971809	13	44	17
44	305975844465	12	39	15
43	276893011713	12	39	15
42	262273188399	12	38	15
41	243737427783	12	38	15
40	129132454159	12	37	15
39	84408212665	11	37	15
38	46499142837	11	36	14
37	43253138565	11	36	14
36	19435516681	11	35	14
35	18805635121	11	35	14
34	17807619361	11	35	14
33	8632935681	10	34	13
32	6662648163	10	33	13
31	1894216583	10	31	12
30	208080483	9	28	11
29	30643095	8	25	10
28	30522135	8	25	10
27	1986127	7	21	9
26	1974031	7	21	9
25	1632995	7	21	8
24	1508381	7	21	8
23	1093281	7	21	8
22	1040319	7	20	8
21	425971	6	19	8
20	180213	6	18	7
19	153513	6	18	7
18	151497	6	18	7
17	148617	6	18	7
16	Prime! 85093	5	17	7
15	66433	5	17	7
14	28539	5	15	6
13	4593	4	13	5
12	4257	4	13	5
11	3999	4	12	5
10	819	3	10	4
9	693	3	10	4
8	427	3	9	4
7	129	3	8	3
6	21	2	5	2
5	Prime! 7	1	3	2
4	Prime! 5	1	3	1
3	Prime! 3	1	2	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 2 and base 7 A182234	L equi 10	L base 2	L base 7

45	144735146046030299112771319	27	87	31
44	128713543915362867228053291	27	87	31
43	80347901032433196717127457	26	87	31
42	52309532921196512044107957	26	86	31
41	2746522115529753005549193	25	82	29
40	2537709652845469133838945	25	82	29
39	2045328483160276032385307	25	81	29
38	1617042324003877388578005	25	81	29
37	471678638661546935436259	24	79	29
36	26432962459781879544013	23	75	27
35	19855989195900063134049	23	75	27
34	1051742679496162996263	22	70	25
33	839909381231478441069	21	70	25
32	3997451286601328571	19	62	23
31	427510260590336957	18	59	21
30	81590995511342857	17	57	21
29	6496728596849949	16	53	19
28	1797708850136627	16	51	19
27	4713161675921	13	43	15
26	3425211644643	13	42	15
25	Prime! 1566399158893	13	41	15
24	72822171105	11	37	13
23	71859215265	11	37	13
22	37344016593	11	36	13
21	24051338445	11	35	13
20	15935958711	11	34	13
19	1052109663	10	30	11
18	22468309	8	25	9
17	19992857	8	25	9
16	12916899	8	24	9
15	786435	6	20	7
14	512607	6	19	7
13	399171	6	19	7
12	210099	6	18	7
11	11757	5	14	5
10	11253	5	14	5
9	9201	4	14	5
8	5049	4	13	5
7	Prime! 257	3	9	3
6	Prime! 107	3	7	3
5	85	2	7	3
4	Prime! 5	1	3	1
3	Prime! 3	1	2	1
2	1	1	1	1
1	0	1	1	1

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

69	27383854659992090708953438128949	32	105	33
68	13299525989953566305481849879525	32	104	33
67	11761942439570181549885533662761	32	104	33
66	325449036571496430311934611137	30	99	31
65	285495032903907768492672121191	30	98	31
64	272636470146897683727270796347	30	98	31
63	267330408442281785103076380651	30	98	31
62	116284153520275827942053886941	30	97	31
61	3313349624824059206539399893	28	92	29
60	3226473616825253131676840805	28	92	29
59	3159242546300009927048702661	28	92	29
58	3141152420006093352888116805	28	92	29
57	Prime! 615850986357618363622206847	27	89	29
56	43204338966326005406289777	26	86	27
55	36331649733825849480459791	26	85	27
54	Prime! 26315683709701629860193397	26	85	27
53	8969756245665011874576055	25	83	27
52	566416282712155854161911	24	79	25
51	536614912484872949318343	24	79	25
50	287582669371604651338191	24	78	25
49	250650845788990615646763	24	78	25
48	242738940902894032509363	24	78	25
47	241441367829916153954611	2	78	25
46	6080900468847014660901	22	73	23
45	2189299497937221630647	22	71	23
44	86214274421074129321	20	67	21
43	1306688242829641865	19	61	19
42	1247103797940661841	19	61	19
41	586178871768257601	18	60	19
40	487154413087025691	18	59	19
39	349013080305074009	18	59	19
38	155315813368497	15	48	15
37	124537880318279	15	47	15
36	82474703167593	14	47	15
35	1616662113341	13	41	13
34	1085079274815	13	40	13
33	1032991588623	13	40	13
32	1030890430479	13	40	13
31	28829406059	11	35	11
30	25726334461	11	35	11
29	25636651261	11	35	11
28	24523959661	11	35	11
27	11022828069	11	34	11
26	6080408749	10	33	11
25	271114881	9	29	9
24	134978817	9	28	9
23	133638015	9	27	9
22	Prime! 90352181	8	27	9
21	67472641	8	27	9
20	4210945	7	23	7
19	3519339	7	22	7
18	2122113	7	22	7
17	1786971	7	21	7
16	1405397	7	21	7
15	1245161	7	21	7
14	42405	5	16	5
13	19929	5	15	5
12	Prime! 19433	5	15	5
11	17057	5	15	5
10	6643	4	13	5
9	455	3	9	3
8	273	3	9	3
7	255	3	8	3
6	Prime! 127	3	7	3
5	Prime! 7	1	3	1
4	Prime! 5	1	3	1
3	Prime! 3	1	2	1
2	1	1	1	1
1	0	1	1	0

Index Nr	Simultaneous palindromic in base 3 and base 4 A097928	L equi 10	L base 3	L base 4

35	174949411464869472111638	24	49	39
34	151289716815885983700994	24	49	39
33	121904971169450717561305	24	49	39
32	13267978780025510037454	23	47	37
31	12419161437212369154346	23	47	37
30	186471757709076102730	21	43	34
29	2330173277374473538	19	39	31
28	1914006557036313769	19	39	31
27	244091990257709863	18	37	29
26	193201488006948586	18	37	29
25	183016579474682506	18	37	29
24	46991827781783450	17	35	28
23	37707959614889810	17	35	28
22	5158488358367585	16	33	27
21	2887846891280410	16	33	26
20	1956592840355065	16	33	26
19	534479689454189	15	31	25
18	55988454554339	14	29	23
17	Prime! 53903615484947	14	29	23
16	635913760790	12	25	20
15	77887660577	11	23	19
14	46746179770	11	23	18
13	1136307905	10	19	16
12	956613659	9	19	15
11	916821671	9	19	15
10	11435450	8	15	12
9	Prime! 1181729	7	13	11
8	749470	6	13	10
7	175850	6	11	9
6	11950	5	9	7
5	130	3	5	4
4	10	2	3	2
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 3 and base 5 A259374	L equi 10	L base 3	L base 5

45	76264883561776274379908	23	48	33
44	32035371021240853343356	23	48	33
43	31557988159203994267456	23	48	33
42	4611589421840328434224	22	46	31
41	2313109014064895895062	22	45	31
40	2072261080808910025382	22	45	31
39	1363633951126304641036	22	45	31
38	105734861679582249272	21	42	29
37	6309131572703144884	19	40	27
36	4962844393339522708	19	40	27
35	2195151134400744286	19	39	27
34	234679042329212848	18	37	25
33	198586101776613958	18	37	25
32	187908509573113078	18	37	25
31	149954769917489312	18	36	25
30	76226057197381156	17	36	25
29	278737550525722	15	31	21
28	158312796835916	15	30	21
27	18432110906024	14	28	19
26	670919564984	12	25	17
25	478999841578	12	25	17
24	201241053056	12	24	17
23	18814619428	11	22	15
22	12814126552	11	22	15
21	9256436186	10	21	15
20	9012701786	10	21	15
19	1065805109	10	19	13
18	320785556	9	18	13
17	33274388	8	16	11
16	27711772	8	16	11
15	26513692	8	16	11
14	14752936	8	16	11
13	437576	6	12	9
12	423176	6	12	9
11	67834	5	11	7
10	32152	5	10	7
9	2188	4	8	5
8	Prime! 1667	4	7	5
7	1066	4	7	5
6	52	2	4	3
5	26	2	3	3
4	4	1	2	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 3 and base 6 A259375	L equi 10	L base 3	L base 6

64	212319152360914299199	21	43	27
63	27584373079009300889	20	41	25
62	25262465853032800967	20	41	25
61	23166722366697502762	20	41	25
60	20926037022213386752	20	41	25
59	20916510485840386576	20	41	25
58	19337874710482930612	20	41	25
57	19337600565718137076	20	41	25
56	378860371017195596	18	37	23
55	342284137776516584	18	37	23
54	341978130563929400	18	37	23
53	97995995365713424	17	36	22
52	97627162288019560	17	36	22
51	95810973516749932	17	36	22
50	49218128293009760	17	35	22
49	17444458374391288	17	35	21
48	17138747829520396	17	35	21
47	2783521300720846	16	33	20
46	608310882180287	15	31	19
45	599852455637939	15	31	19
44	599825258665811	15	31	19
43	512166253983233	15	31	19
42	81041908142188	14	30	18
41	27950430282103	14	29	18
40	11610051837124	14	28	17
39	5817003372578	13	27	17
38	5816975658914	13	27	17
37	2947903946317	13	27	17
36	333349186006	12	25	15
35	232039258376	12	24	15
34	232018753064	12	24	15
33	231852949304	12	24	15
32	201669082004	12	24	15
31	201509576804	12	24	15
30	200316968444	12	24	15
29	200267707484	12	24	15
28	28476193256	11	22	14
27	539212009	9	19	12
26	Prime! 78526951	8	17	11
25	77894071	8	17	11
24	8271430	7	15	9
23	8128762	7	15	9
22	7723642	7	15	9
21	6927700	7	15	9
20	6877120	7	15	9
19	6731644	7	15	9
18	225064	6	12	7
17	221068	6	12	7
16	122420	6	11	7
15	87763	5	11	7
14	74647	5	11	7
13	34972	5	10	6
12	34216	5	10	6
11	910	3	7	4
10	644	3	6	4
9	560	3	6	4
8	203	3	5	3
7	160	3	5	3
6	80	2	4	3
5	28	2	4	2
4	4	1	2	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 3 and base 7 A259377	L equi 10	L base 3	L base 7

87	2939144234733141879192412	25	52	29
86	2272476265566123596598532	25	52	29
85	1629258710898659034459800	25	51	29
84	736301183207717787147244	24	51	29
83	644449513925853629058500	24	50	29
82	553658983693788118137356	24	50	29
81	400341897012900468065488	24	50	28
80	378346857606056071274512	24	50	28
79	343550873981934470383600	24	50	28
78	37790674156897878083620	23	48	27
77	24871504126683981647015	23	47	27
76	20202287143923694819172	23	47	27
75	19792663061377198446029	23	47	27
74	14492914970724913820791	23	47	27
73	12740373453026608614499	23	47	27
72	979838454518061976304	21	44	25
71	314121124263032247050	21	43	25
70	175469998392732393832	21	43	24
69	83996138774758424168	20	42	24
68	74378389632102455888	20	42	24
67	71005734774446229088	20	42	24
66	24633761312367628301	20	41	23
65	17263015931639807599	20	41	23
64	11517148240701376184	20	40	23
63	1555316911250634016	19	39	22
62	988421346024174056	18	38	22
61	418138444696392656	18	37	21
60	332251822186446404	18	37	21
59	320754726799278860	18	37	21
58	315307247753837405	18	37	21
57	276769804176685816	18	37	21
56	145103278493444048	18	36	21
55	70150821079952416	17	36	20
54	31966439598053368	17	35	20
53	14959744316064584	17	34	20
52	11207352411046784	17	34	19
51	6410639089100872	16	34	19
50	3959720840467478	16	33	19
49	3660645308508736	16	33	19
48	2921460800777086	16	33	19
47	1734195226323428	16	32	19
46	1560764115683240	16	32	18
45	429162107575160	15	31	18
44	45221839119556	14	29	17
43	22666883572232	14	28	16
42	21772277941544	14	28	16
41	17136683996456	14	28	16
40	830172165614	12	25	15
39	469837033600	12	25	14
38	68095147754	11	23	13
37	65304259157	11	23	13
36	11641189600	11	22	12
35	5642510512	10	21	12
34	4346524576	10	21	12
33	184827640	9	18	10
32	87001616	8	17	10
31	35664908	8	16	9
30	24919360	8	16	9
29	11502842	8	15	9
28	3316520	7	14	8
27	2585488	7	14	8
26	741586	6	13	7
25	639721	6	13	7
24	532900	6	13	7
23	233920	6	12	7
22	112048	6	11	6
21	108016	6	11	6
20	76024	5	11	6
19	54008	5	10	6
18	14762	5	9	5
17	Prime! 9103	4	9	5
16	8200	4	9	5
15	1312	4	7	4
14	400	3	6	4
13	328	3	6	3
12	242	3	5	3
11	164	3	5	3
10	142	3	5	3
9	121	3	5	3
8	100	3	5	3
7	40	2	4	2
6	16	2	3	2
5	8	1	2	2
4	4	1	2	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 3 and base 8 A259381	L equi 10	L base 3	L base 8

43	364695395569897227580	21	44	23
42	360014620577548665916	21	44	23
41	330300143900971857820	21	44	23
40	304720541325476344844	21	43	23
39	249655679139170920475	21	43	23
38	249636212093446658075	21	43	23
37	196406739090043790506	21	43	23
36	195149355943974110314	21	43	23
35	153561319370542367554	21	43	23
34	150326844251484391042	21	43	23
33	120014682355984031785	21	43	23
32	5741752257294068668	19	40	21
31	4949458745712184468	19	40	21
30	2999263443800192930	19	39	21
29	2959907850689099042	19	39	21
28	79174156601271388	17	36	19
27	73083110864755396	17	36	19
26	44880998812567514	17	35	19
25	2127271328430823	16	33	17
24	363376288168081	15	31	17
23	21056462595764	14	28	15
22	419572845958	12	25	13
21	81473867465	11	23	13
20	81452592329	11	23	13
19	5691134677	10	21	11
18	4099065139	10	21	11
17	67470916	8	17	9
16	58961443	8	17	9
15	Prime! 1554173	7	13	7
14	1276916	7	13	7
13	1141652	7	13	7
12	944035	6	13	7
11	17492	5	9	5
10	9490	4	9	5
9	8578	4	9	5
8	316	3	6	3
7	203	3	5	3
6	130	3	5	3
5	121	3	5	3
4	4	1	2	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

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

36	217492970066095627136046	24	39	34
35	12454588508239508448042	23	37	32
34	12009763459975975060362	23	37	32
33	11320022857296028412262	23	37	32
32	11025274475869249136982	23	37	32
31	65738451925934654491	20	33	29
30	50248128332089611706	20	33	29
29	49903539441293379706	20	33	29
28	41186255976066325426	20	33	29
27	Prime! 4390844685981744847	19	31	27
26	Prime! 250855520885240759	18	29	25
25	234602176132265223	18	29	25
24	5892002867556037	16	27	23
23	383478037564629	15	25	21
22	48517516968462	14	23	20
21	47470618709562	14	23	20
20	37004798195346	14	23	20
19	3101308506654	13	21	18
18	2806999337418	13	21	18
17	155784877126	12	19	17
16	16619231967	11	17	15
15	16516113567	11	17	15
14	Prime! 32317933	8	13	11
13	25651017	8	13	11
12	17402241	8	13	11
11	17099841	8	13	11
10	2593206	7	11	10
9	2347506	7	11	10
8	193662	6	9	8
7	76449	5	9	7
6	9222	4	7	6
5	46	2	3	3
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 4 and base 6 A259376	L equi 10	L base 4	L base 6

64	727070725217607363190	21	35	27
63	716609877969961732582	21	35	27
62	284110399839401441695	21	34	27
61	258942009983706473995	21	34	27
60	24025722803574072773	20	33	25
59	11550098019396133130	20	32	25
58	4452455483471325407	19	31	24
57	1179899868668886337	19	31	24
56	636351200832860530	18	30	23
55	523628978023895325	18	30	23
54	509127549196054605	18	30	23
53	434259874286090505	18	30	23
52	127154149795232525	18	29	22
51	80394116386707921	17	29	22
50	72073074246336513	17	29	22
49	10023898627083698	17	27	21
48	9998493962835122	16	27	21
47	933118742276119	15	25	20
46	550117934650493	15	25	19
45	404400465825765	15	25	19
44	403705181414373	15	25	19
43	329536806222753	15	25	19
42	323292550693473	15	25	19
41	46164680151002	14	23	18
40	30255762326713	14	23	18
39	15822654274715	14	22	17
38	12887266632430	14	22	17
37	12761538567790	14	22	17
36	11931403417210	14	22	17
35	2281658774290	13	21	16
34	1809863435625	13	21	16
33	401478741365	12	20	15
32	270747359295	12	19	15
31	186398221946	12	19	15
30	107074105033	12	19	15
29	12982275395	11	17	13
28	9330794722	10	17	13
27	9233901154	10	17	13
26	4165108015	10	16	13
25	4036503055	10	16	13
24	3614009815	10	16	13
23	Prime! 322509617	9	15	11
22	231755895	9	14	11
21	223892055	9	14	11
20	33348861	8	13	10
19	5494725	7	12	9
18	3314083	7	11	9
17	1856845	7	11	9
16	196606	6	9	7
15	Prime! 69313	5	9	7
14	14539	5	7	6
13	12691	5	7	6
12	Prime! 7517	4	7	5
11	7373	4	7	5
10	1885	4	6	5
9	819	3	5	4
8	215	3	4	3
7	55	2	3	3
6	21	2	3	2
5	Prime! 5	1	2	1
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 4 and base 7 A259378	L equi 10	L base 4	L base 7

57	63995036322697967539289799	26	43	31
56	47566482518578810820594038	26	43	31
55	27587024291623263689560549	26	43	31
54	2638896559442399728684770	25	41	29
53	1432896717582234021128161	25	41	29
52	1176137521373269234724975	25	40	29
51	25832614487515353354965	23	38	27
50	13582685517334809482286	23	37	27
49	10901860119248612490950	23	37	27
48	926561758657919494947	21	35	25
47	818394448405038406990	21	35	25
46	203976863667466529550	21	34	25
45	13773316835159709950	20	32	23
44	12007980674606373530	20	32	23
43	6017746453312946885	19	32	23
42	4218808128230591659	19	31	23
41	241521030849544855	18	29	21
40	188077235829465306	18	29	21
39	185569961319483162	18	29	21
38	10556338547376278	17	27	19
37	10490343658800214	17	27	19
36	6109256963409813	16	27	19
35	4467627704385	13	22	15
34	3628335729863	13	21	15
33	3304611554563	13	21	15
32	3205015384750	13	21	15
31	2047644601565	13	21	15
30	1871644872505	13	21	15
29	1134972961921	13	21	15
28	1103782149121	13	21	15
27	30592589645	11	18	13
26	22182595205	11	18	13
25	1692399385	10	16	11
24	742494286	9	15	11
23	640680742	9	15	11
22	430421657	9	15	11
21	Prime! 424623193	9	15	11
20	387973685	9	15	11
19	34179458	8	13	9
18	31946605	8	13	9
17	9262450	7	12	9
16	786435	6	10	7
15	428585	6	10	7
14	189806	6	9	7
13	14811	5	7	5
12	13655	5	7	5
11	9958	4	7	5
10	8802	4	7	5
9	Prime! 257	3	5	3
8	235	3	4	3
7	150	3	4	3
6	85	2	4	3
5	Prime! 5	1	2	1
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

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

57	750791439727272752010	21	35	22
56	655054067808976740530	21	35	22
55	97830227132597053205	20	34	21
54	55327341317278801918	20	33	21
53	53694063656991154606	20	33	21
52	53526713487999458926	20	33	21
51	Prime! 22346657910193902193	20	33	21
50	11303748773839091510	20	32	20
49	10552570503887949190	20	32	20
48	287411961823187455	18	29	19
47	16046526958346267	17	27	17
46	12173822386241658	17	27	17
45	9888480378524210	16	27	17
44	4728069796793537	16	27	17
43	2172761848365805	16	26	17
42	2114967436733485	16	26	17
41	743215116795690	15	25	16
40	204973846313390	15	24	15
39	198777976021790	15	24	15
38	84470553495345	14	24	15
37	38244097345762	14	23	15
36	11372760382810	14	22	14
35	11356994802010	14	22	14
34	9295288254930	13	22	14
33	2292918574418	13	21	13
32	1014966912315	13	20	13
31	902465909895	12	20	13
30	204283593150	12	19	12
29	174913133450	12	19	12
28	160142137430	12	19	12
27	6899910553	10	17	11
26	6852736153	10	17	11
25	2299011170	10	16	10
24	163490790	9	14	9
23	9971750	7	12	8
22	4210945	7	12	7
21	3080174	7	11	7
20	3027758	7	11	7
19	2576758	7	11	7
18	1898445	7	11	7
17	Prime! 1181729	7	11	7
16	54215	5	8	5
15	23205	5	8	5
14	Prime! 16319	5	7	5
13	2910	4	6	4
12	2730	4	6	4
11	2550	4	6	4
10	546	3	5	3
9	Prime! 373	3	5	3
8	273	3	5	3
7	255	3	4	3
6	10	2	2	2
5	Prime! 5	1	2	1
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 5 and base 6 A097930	L equi 10	L base 5	L base 6

43	1011875381060617752551	22	31	27
42	166139675801802801539	21	29	26
41	132450774427686689338	21	29	26
40	6092831596205037679	19	27	25
39	4934883644169952933	19	27	25
38	4384942329377565347	19	27	24
37	269196579469276814	18	25	23
36	190645138816971853	18	25	23
35	141417349010810857	18	25	23
34	128031593329179827	18	25	22
33	9779924118261554	16	23	21
32	3099677168429681	16	23	20
31	451853066660344	15	21	19
30	275956595195822	15	21	19
29	4262839618051	13	19	17
28	341225573632	12	17	15
27	330347455102	12	17	15
26	303520083621	12	17	15
25	246467321391	12	17	15
24	240971251611	12	17	15
23	204185363456	12	17	15
22	198522549056	12	17	15
21	402327541	9	13	12
20	297379006	9	13	11
19	295979506	9	13	11
18	48616624	8	11	10
17	883407	6	9	8
16	755846	6	9	8
15	723296	6	9	8
14	704396	6	9	8
13	27741	5	7	6
12	26691	5	7	6
11	3074	4	5	5
10	Prime! 2293	4	5	5
9	651	3	5	4
8	104	3	3	3
7	98	2	3	3
6	Prime! 67	2	3	3
5	4	1	1	1
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 5 and base 7 A249156	L equi 10	L base 5	L base 7

85	1256031294979348958308702	25	35	29
84	1066391919678134643984896	25	35	29
83	1047531737761472233043741	25	35	29
82	431184915313742016296568	24	34	28
81	191971143478439368681416	24	34	28
80	91956582424491712914848	23	33	28
79	61910549215322379497792	23	33	27
78	40851647091858572666841	23	33	27
77	39695632789437991162941	23	33	27
76	37637504634853696144016	23	33	27
75	8362079157242442395616	22	32	26
74	3695400097492315843248	22	31	26
73	2409216715720544526112	22	31	26
72	1256193516603697424206	22	31	25
71	1191911601483144093656	22	31	25
70	501421356545418476442	21	30	25
69	486267340125277760142	21	30	25
68	348557712481567649796	21	30	25
67	97411522344257146392	20	29	24
66	18273867034949670162	20	28	23
65	6139100437190687429	19	27	23
64	4854611133682563408	19	27	23
63	4074872026917237092	19	27	23
62	3473187009111400832	19	27	22
61	2421099236773866016	19	27	22
60	238359847236631248	18	25	21
59	110535513802830796	18	25	21
58	55358830255457544	17	24	20
57	32369820521361192	17	24	20
56	8491231634043863	16	23	19
55	8152267045954638	16	23	19
54	7858433687515933	16	23	19
53	6746177019008522	16	23	19
52	5784321085207262	16	23	19
51	4951212613811152	16	23	19
50	850046505221616	15	22	18
49	298887675308328	15	21	18
48	179568939231946	15	21	17
47	37465698385746	14	20	17
46	Prime! 4359505255951	13	19	15
45	364482389232	12	17	14
44	147445356024	12	16	14
43	65252488452	11	16	13
42	28581869444	11	15	13
41	17493894797	11	15	13
40	7721681656	10	15	12
39	4191009888	10	14	12
38	1692569856	10	14	11
37	1680662856	10	14	11
36	1621093206	10	14	11
35	764059578	9	13	11
34	663706192	9	13	11
33	159690408	9	12	10
32	39280254	8	11	9
31	Prime! 34853363	8	11	9
30	34713713	8	11	9
29	22412057	8	11	9
28	18108296	8	11	9
27	17968646	8	11	9
26	1862744	7	9	8
25	1823544	7	9	8
24	1636104	7	9	8
23	1473368	7	9	8
22	1434168	7	9	8
21	769621	6	9	7
20	593836	6	9	7
19	537856	6	9	7
18	100056	6	8	6
17	27616	5	7	6
16	12654	5	6	5
15	10308	5	6	5
14	1432	4	5	4
13	856	3	5	4
12	624	3	4	4
11	342	3	4	3
10	114	3	3	3
9	78	2	3	3
8	57	2	3	3
7	24	2	2	2
6	6	1	2	1
5	4	1	1	1
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 5 and base 8 A259383	L equi 10	L base 5	L base 8

67	515771636274389087742	21	30	23
66	489739517365774724142	21	30	23
65	483298841095537541862	21	30	23
64	467299175833745311062	21	30	23
63	75003753306379661377	20	29	23
62	44026278992431183476	20	29	22
61	23183943016281734178	20	28	22
60	6205436790382323229	19	27	21
59	6018014891186143629	19	27	21
58	4952676794849410708	19	27	21
57	4367927778916423347	19	27	21
56	3127137795707197802	19	27	21
55	927609347442003678	18	26	20
54	873874206536745222	18	26	20
53	108722249102656646	18	25	19
52	87070543138674036	17	25	19
51	72229221342410756	17	25	19
50	63919308246503651	17	25	19
49	54018307498782714	17	24	19
48	48200460817298154	17	24	19
47	15215146816292406	17	24	18
46	14586052232559006	17	24	18
45	10610347035085164	17	23	18
44	8630118003254643	16	23	18
43	4179976145681841	16	23	18
42	1837422543645798	16	22	17
41	1167704597006412	16	22	17
40	610409921031306	15	22	17
39	325005646077513	15	21	17
38	14952142559323	14	19	15
37	11073162740322	14	19	15
36	8866678870082	13	19	15
35	5809320306961	13	19	15
34	1284108810066	13	18	14
33	1274936571666	13	18	14
32	669367713609	12	17	14
31	469606524278	12	17	13
30	176616961826	12	17	13
29	139853034114	12	16	13
28	42360367356	11	16	12
27	7300948726	10	15	11
26	5067084204	10	14	11
25	5018349804	10	14	11
24	2459962002	10	14	11
23	716064597	9	13	10
22	621319212	9	13	10
21	551366532	9	13	10
20	257161401	9	13	10
19	32285433	8	11	9
18	5359842	7	10	8
17	563786	6	9	7
16	228222	6	8	6
15	151596	6	8	6
14	18076	5	7	5
13	11898	5	6	5
12	2709	4	5	4
11	2268	4	5	4
10	438	3	4	3
9	186	3	4	3
8	36	2	3	2
7	18	2	2	2
6	6	1	2	1
5	4	1	1	1
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 5 and base 9 A259388	L equi 10	L base 5	L base 9

40	1813372452478843107346	22	31	23
39	82763508198753336507	20	29	21
38	42838465487714339826	20	29	21
37	960588069334571508	18	26	19
36	911840478745176528	18	26	19
35	256320146951057809	18	25	19
34	6284871831461142	16	23	17
33	6221009414075142	16	23	17
32	5744620259340762	16	23	17
31	4287997640956241	16	23	17
30	145464252692586	15	21	15
29	137416991943786	15	21	15
28	71088928149468	14	20	15
27	70942565653068	14	20	15
26	26358878059	11	15	11
25	24863844904	11	15	11
24	24208576998	11	15	11
23	20134447808	11	15	11
22	19671459008	11	15	11
21	12607012902	11	15	11
20	1677684	7	9	7
19	1412768	7	9	7
18	1313858	7	9	7
17	1142597	7	9	7
16	48553	5	7	5
15	Prime! 47653	5	7	5
14	41667	5	7	5
13	32152	5	7	5
12	22386	5	7	5
11	Prime! 701	3	5	3
10	564	3	4	3
9	282	3	4	3
8	246	3	4	3
7	Prime! 109	3	3	3
6	6	1	2	1
5	4	1	1	1
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 6 and base 7 A097931	L equi 10	L base 6	L base 7

50	763935242386707102652	21	27	25
49	668496304052005621965	21	27	25
48	479871791497878191414	21	27	25
47	255450059055825463705	21	27	25
46	26089964728430283743	20	25	23
45	24835713299768685971	20	25	23
44	24339885317146470749	20	25	23
43	10684777862880029708	20	25	23
42	10324628539087401800	20	25	23
41	8908237172623238851	19	25	23
40	418394899248730857	18	23	21
39	411331566980657307	18	23	21
38	373054804455006608	18	23	21
37	223438058101993597	18	23	21
36	163830160024067455	18	23	21
35	10231408608585002	17	21	19
34	10229280954883514	17	21	19
33	6875219172190387	16	21	19
32	6116904274791985	16	21	19
31	126532386891655	15	19	17
30	13267882222408	14	17	16
29	12262956787888	14	17	16
28	4102350269485	13	17	15
27	321015775216	12	15	14
26	231773764784	12	15	14
25	204191148800	12	15	14
24	203509031168	12	15	14
23	9689802280	10	13	12
22	160258808	9	11	10
21	4252232	7	9	8
20	279071	6	7	7
19	271721	6	7	7
18	269957	6	7	7
17	213970	6	7	7
16	206620	6	7	7
15	204856	6	7	7
14	186621	6	7	7
13	Prime! 7703	4	5	5
12	6148	4	5	5
11	5854	4	5	5
10	185	3	3	3
9	178	3	3	3
8	135	3	3	3
7	92	2	3	3
6	Prime! 5	1	1	1
5	4	1	1	1
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 6 and base 8 A259384	L equi 10	L base 6	L base 8

74	587636422553353669503	21	27	23
73	537799059792585250455	21	27	23
72	527746494866314721871	21	27	23
71	470473355044455858206	21	27	23
70	226800596470478658307	21	27	23
69	15385536281457855657	20	25	22
68	15292492682301599913	20	25	22
67	15055878270585464361	20	25	22
66	6676995959002864309	19	25	21
65	6670196618287715509	19	25	21
64	6604592701475687341	19	25	21
63	4610858255198740475	19	24	21
62	4464556519216209395	19	24	21
61	1373896414642050313	19	24	21
60	1331874276783373897	19	24	21
59	498683205468936027	18	23	20
58	485893308196560339	18	23	20
57	53493764633670074	17	22	19
56	31629295131227185	17	22	19
55	24642663243594193	17	22	19
54	21316861847661257	17	21	19
53	18474790776900161	17	21	19
52	12165877883083869	17	21	18
51	11951590146783957	17	21	18
50	11716742258786637	17	21	18
49	2098982030706015	16	20	17
48	926464106240659	15	20	17
47	516268720555889	15	19	17
46	401205063672537	15	19	17
45	371039856325905	15	19	17
44	55584258482529	14	18	16
43	33004205249575	14	18	15
42	24722285628901	14	18	15
41	Prime! 15813860880803	14	17	15
40	15804478291811	14	17	15
39	11760498311914	14	17	15
38	4920262093249	13	17	15
37	1756866976011	13	16	14
36	396619220597	12	15	13
35	318743407660	12	15	13
34	186431605610	12	15	13
33	166787896538	12	15	13
32	Prime! 116755331881	12	15	13
31	116606986537	12	15	13
30	108218625313	12	15	13
29	88574916241	11	15	13
28	80375377033	11	15	13
27	43253138565	11	14	12
26	8094406311	10	13	11
25	4061216947	10	13	11
24	3292861699	10	13	11
23	3286138051	10	13	11
22	2115191225	10	12	11
21	1830945641	10	12	11
20	1420737297	10	12	11
19	119204743	9	11	9
18	84572293	8	11	9
17	56939099	8	10	9
16	46823602	8	10	9
15	1032507	7	8	7
14	567434	6	8	7
13	315721	6	8	7
12	7409	4	5	5
11	5001	4	5	5
10	203	3	3	3
9	178	3	3	3
8	154	3	3	3
7	Prime! 7	1	2	1
6	Prime! 5	1	1	1
5	4	1	1	1
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 6 and base 9 A259389	L equi 10	L base 6	L base 9

57	1672349967949028125555	22	28	23
56	1637103709482544478791	22	28	23
55	841776858189016532710	21	27	22
54	837963541719726071650	21	27	22
53	Prime! 25237844535689857919	20	25	21
52	20526982298523749494	20	25	21
51	468242151115317501	18	23	19
50	340926523717507544	18	23	19
49	203861282386826791	18	23	19
48	202186253210480911	18	23	19
47	197907886640180179	18	23	19
46	12414212677911183	17	21	17
45	10915838736621332	17	21	17
44	10841022411090800	17	21	17
43	10796808110179352	17	21	17
42	10790519823772232	17	21	17
41	10674979690311068	17	21	17
40	10666075534207052	17	21	17
39	1658410356393350	16	20	16
38	27832011695551	14	18	15
37	7264479038060	13	17	14
36	327925630018	12	15	13
35	187195815770	12	15	12
34	185794441250	12	15	12
33	184314116750	12	15	12
32	55854298990	11	14	12
31	124443290	9	11	9
30	124091822	9	11	9
29	123427622	9	11	9
28	69432517	8	11	9
27	Prime! 61281793	8	11	9
26	48307924	8	10	9
25	7971580	7	9	8
24	2515513	7	9	7
23	2494129	7	9	7
22	2488945	7	9	7
21	2439445	7	9	7
20	2350165	7	9	7
19	2300665	7	9	7
18	Prime! 2295481	7	9	7
17	16814	5	6	5
16	16562	5	6	5
15	8281	4	6	5
14	5740	4	5	4
13	3740	4	5	4
12	910	3	4	4
11	209	3	3	3
10	Prime! 191	3	3	3
9	154	3	3	3
8	80	2	3	2
7	Prime! 7	1	2	1
6	Prime! 5	1	1	1
5	4	1	1	1
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 7 and base 8 A099145	L equi 10	L base 7	L base 8

48	543174425539340174295	21	25	23
47	432746793552539117045	21	25	23
46	423479048759927584237	21	25	23
45	353873672982519332532	21	25	23
44	299136638137274062532	21	25	23
43	290293502938358099195	21	25	23
42	277786634125993659955	21	25	23
41	10688365729164780	17	19	18
40	6641481107049786	16	19	18
39	6622944330543930	16	19	18
38	6615812399178042	16	19	18
37	68995850733945	14	17	16
36	4712469842177	13	15	15
35	3741580511478	13	15	14
34	55027793502	11	13	12
33	54464523606	11	13	12
32	54453459798	11	13	12
31	1709813601	10	11	11
30	1556085529	10	11	11
29	630832428	9	11	10
28	27924649	8	9	9
27	10453500	8	9	8
26	786435	6	7	7
25	626778	6	7	7
24	502457	6	7	7
23	450985	6	7	7
22	447849	6	7	7
21	Prime! 444713	6	7	7
20	431721	6	7	7
19	428585	6	7	7
18	16708	5	5	5
17	13459	5	5	5
16	10658	5	5	5
15	7801	4	5	5
14	6953	4	5	5
13	2997	4	5	4
12	300	3	3	3
11	292	3	3	3
10	235	3	3	3
9	178	3	3	3
8	121	3	3	3
7	6	1	1	1
6	Prime! 5	1	1	1
5	4	1	1	1
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 7 and base 9 A259390	L equi 10	L base 7	L base 9

86	854993738873524179850	21	25	22
85	512072044301517020050	21	25	22
84	92520418698791396512	20	24	21
83	47987409188845232688	20	24	21
82	18419097769705052893	20	23	21
81	12346857701296110730	20	23	21
80	6704825946724092370	19	23	20
79	3507460573508033960	19	22	20
78	2945908644901976360	19	22	20
77	2767723069416266000	19	22	20
76	1153224512261940400	19	22	19
75	993715719098312400	18	22	19
74	568376956845068736	18	22	19
73	511220556702236100	18	21	19
72	432621948882842255	18	21	19
71	282488203379766646	18	21	19
70	208201514372069311	18	21	19
69	165908503654004197	18	21	19
68	63100241427288000	17	20	18
67	11132375103763458	17	19	17
66	10368492428697080	17	19	17
65	9812330223915785	16	19	17
64	9350709125459378	16	19	17
63	6221745601065984	16	19	17
62	1993926853603000	16	19	17
61	1104575959129640	16	18	16
60	834424022498440	15	18	16
59	811740650692800	15	18	16
58	734723345582040	15	18	16
57	206576333227900	15	17	16
56	172921319185669	15	17	15
55	147993832352958	15	17	15
54	68503313361800	14	17	15
53	20268849562000	14	16	14
52	2088800185930	13	15	13
51	1202029647736	13	15	13
50	796259955485	12	15	13
49	84668107250	11	13	12
48	83714515310	11	13	12
47	30862471355	11	13	11
46	22668403353	11	13	11
45	Prime! 20537111057	11	13	11
44	20404027400	11	13	11
43	15127811455	11	13	11
42	13575144288	11	12	11
41	2225211080	10	12	10
40	1684866370	10	11	10
39	194062432	9	10	9
38	22674550	8	9	8
37	12990350	8	9	8
36	4084000	7	8	7
35	3501600	7	8	7
34	3344352	7	8	7
33	2913368	7	8	7
32	2756120	7	8	7
31	738100	6	7	7
30	555013	6	7	7
29	532900	6	7	7
28	400200	6	7	6
27	201720	6	7	6
26	164900	6	7	6
25	45600	5	6	5
24	22800	5	6	5
23	14762	5	5	5
22	14510	5	5	5
21	10252	5	5	5
20	8200	4	5	5
19	3550	4	5	4
18	2000	4	4	4
17	400	3	4	3
16	328	3	3	3
15	300	3	3	3
14	264	3	3	3
13	200	3	3	3
12	164	3	3	3
11	100	3	3	3
10	50	2	3	2
9	40	2	2	2
8	8	1	2	1
7	6	1	1	1
6	Prime! 5	1	1	1
5	4	1	1	1
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Index Nr	Simultaneous palindromic in base 8 and base 9 A099146	L equi 10	L base 8	L base 9

54	512918878693453369150	21	23	22
53	359804954513570058300	21	23	22
52	326364387585946501340	21	23	22
51	215424957893108952250	21	23	22
50	206181182637627497650	21	23	22
49	5111391307202132700	19	21	20
48	1205520295345991297	19	21	19
47	120168724989001390	18	19	18
46	81877825421774500	17	19	18
45	2229560302980799	16	17	17
44	1939137135947326	16	17	17
43	1767662936108630	16	17	16
42	1366179755723700	16	17	16
41	33181029690535	14	15	15
40	31285221426631	14	15	15
39	19404342621340	14	15	14
38	485724124423	12	13	13
37	422454576718	12	13	13
36	318713056300	12	13	13
35	5170508596	10	11	11
34	98383349	8	9	9
33	71877268	8	9	9
32	63367795	8	9	9
31	2067519	7	7	7
30	1405397	7	7	7
29	1373645	7	7	7
28	Prime! 1368461	7	7	7
27	1294652	7	7	7
26	1273268	7	7	7
25	1268084	7	7	7
24	1262900	7	7	7
23	1257716	7	7	7
22	926371	6	7	7
21	899803	6	7	7
20	894619	6	7	7
19	889435	6	7	7
18	27310	5	5	5
17	17876	5	5	5
16	Prime! 12547	5	5	5
15	11314	5	5	5
14	455	3	3	3
13	446	3	3	3
12	Prime! 373	3	3	3
11	300	3	3	3
10	Prime! 227	3	3	3
9	154	3	3	3
8	Prime! 7	1	1	1
7	6	1	1	1
6	Prime! 5	1	1	1
5	4	1	1	1
4	Prime! 3	1	1	1
3	Prime! 2	1	1	1
2	1	1	1	1
1	0	1	1	1

Base 3 and base 9

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
k	in base 3	in base 9
1	0	0
2	1	1
3	11	4
4	101	11
5	202	22
7	2002
13	111111	444
14		555
15	202202
40	112121211
121		488884
393	201000222000102
497	1102111111112011
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 :
On General Palindromic Numbers

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
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

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Patrick De Geest - Belgium

- Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com