World!Of
Numbers

WON plate
225 |

[ June 4, 2023 ] [ Last update September 30, 2023 ]
Building a relationship between the natural numbers
and the ninedigitals using the function
"Prepending n digits d to k so that [d^^n][k]
becomes a record delayed prime
"
Patrick De Geest

When I use the term ninedigital in this plate I always refer to
a strictly zeroless pandigital (digits from 1 to 9 each appearing just once).

( '^^' is symbol for concatenation )

This plate is in fact an offshoot from the material presented in
WONplate 197 (appending digits to k) & more in particular
WONplate 224 (prepending digits to k). So my advise to get
familiarized with the topic presented in those plates.

In plate 197 one can only append digits 1, 3, 7 and 9 to arrive at (probable) primes
whereas in WONplate 224 one can prepend all the nine digits to k. So we will
continue only with the latter because that gives already a clue for arriving
at our ninedigitals. All will become clear with a couple of examples.

Example 1
Start eg. with prepending 50 digits d's (n=50) to k and find its value so that their
concatenation yield a prime or PRP with the extra condition that all smaller numbers n
from 1 to 49 (n-1) yield only composites. Formally we present this as [d^^n][k].
Now let us replace d with the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9. We get:

 Ordered by digits d [1^^50][5433] [2^^50][1479] [3^^50][14183] [4^^50][27] [5^^50][6547] [6^^50][17441] [7^^50][3791] [8^^50][8707] [9^^50][361] Ordered by k from low to high [4^^50][27] [9^^50][361] [2^^50][1479] [7^^50][3791] [1^^50][5433] [5^^50][6547] [8^^50][8707] [3^^50][14183] [6^^50][17441]
Here we see the genesis of our ninedigital outcome
namely read from top to bottom 492715836 that was
generated from our 'seed' the natural number 50.
The next right column will show the reversed ninedigital
i.e. when read from bottom to top (to be constructed yet).

Among these k-values we notice that two of them are prime
so the primescore for seed 50 is 2/9.
In short we were able using this surjective function
to relate seed 50 with ninedigital 492715836 !
And we can do this for all seeds though large seeds will
take a longer time to calculate its k-value then smaller ones.
As they are infinite seeds available and only 9! or 362880 ninedigitals
we can conclude that many seeds lead to the same ninedigital giving us
the opportunity to create lots of sequences...

Example 2
This time our seed will be 'the number of the beast' 666.

 Ordered by digits d [1^^666][302257] [2^^666][286543] [3^^666][148739] [4^^666][181751] [5^^666][67237] [6^^666][1119817] [7^^666][2557] [8^^666][249239] [9^^666][1703279] Ordered by k from low to high [7^^666][2557] [5^^666][67237] [3^^666][148739] [4^^666][181751] [8^^666][249239] [2^^666][286543] [1^^666][302257] [6^^666][1119817] [9^^666][1703279]
Seed 666 yield ninedigital 753482169 with primescore 4/9.

Example 3
Let us search for the ninedigital of the year 2023.

 Ordered by digits d [1^^2023][770407] [2^^2023][437349] [3^^2023][9806093] [4^^2023][1017813] [5^^2023][1961333] [6^^2023][9390491] [7^^2023][1189353] [8^^2023][899151] [9^^2023][5137583] Ordered by k from low to high [2^^2023][437349] [1^^2023][770407] [8^^2023][899151] [4^^2023][1017813] [7^^2023][1189353] [5^^2023][1961333] [9^^2023][5137583] [6^^2023][9390491] [3^^2023][9806093]
So 2023 yield ninedigital 218475963 with alas a primescore of 0/9.

Here is some homework for my readers. Beware that it might be hard
as high seeds needs lots of time to calculate. But PRP's are accepted.

1. Find a ninedigital duo with 2 or more seeds.
 714285936 & 639582417 → 36, 1991, …
2. Find more seeds with a primescore 9/9.
3. Find the seeds for ninedigitals 123456789 and/or 987654321
or that comes closest to these boundaries.
4. Find a record seed that yield 2 to 9 identical k's
be it prime or composite.
 Seed 343 → Two identical k's →
5. Find record k's value tout court per digit from 1 to 9
digit dSeedrecord k
122223227151
213001115589
3222210858933
415001210711
520231961333
6333317313571
733335981041
81700987537
9195610921759
6. Find the first seed with a ninedigital sum of k's (hard).
7. Complete the next sequence with a few more terms
whereby the smallest k ⩽ seed.
1, 2, 3, 11, 15, 17, 30, 50, 68, 69, 77, 161, 173, 182, 187,
204, 240, 300, 353, ...

seedninedigital
from LO to HI
ninedigital
from HI to LO
prime-
score
ordered k's
some peculiarities
Sum of k's
11346725899852764314/9, , , , , , , , 721
28925417366371452986/9, , , , 9, , , 19, 37115
32578416933961487527/91, , , 13, 17, 19, 29, 61, 77239
49173648255284637195/917, 21, 37, 41, 49, , , 89, 149541
52985147366374158926/919, 43, 51, 67, 69, 71, 107, 143, 227797
65182497366379428159/917, , , 53, 59, 107, 227, 293, 3491187
74735981622618953742/937, 99, 127, 129, 253, 299, 343, 407, 4892183
84835621799712653845/929, 91, , , 259, 313, 371, 533, 6472557
94789261533516298746/913, 67, 127, 143, 169, 209, 281, 389, 9532351
105792648133184629755/951, 111, 179, 191, 251, 277, 333, 441, 11632997
115784216933961248754/91, 71, 141, 143, 181, 591, 641, 1051, 14414261
128465712399321756488/989, 107, 127, 137, 179, 389, 667, 1117, 12894101
136251498733789415263/9283, 407, 539, 541, 559, 641, 717, 957, 12615905
145187439622693478154/939, 107, 189, 381, 411, 689, 919, 1229, 16095573
154956827311372865945/911, 121, 161, 181, 281, 359, 503, 841, 1111
Related to ninedigital 345762198 since its decomposition into
a * bcdefghi (3 * 45762198) returns our initial reversed ninedigital.
Source → (J. Heynderickx)
3569
161964253877835246913/9111, 263, 281, 333, 413, 423, 553, 881, 14174675
171548792633629784514/911, 33, 227, 253, 729, 1021, 1141, 1397, 15716383
187615249833894251679/929, 149, 179, 271, 353, 367, 383, 1063, 16374431
191895732466423759811/9, , 407, 893, 1111, 1433, 1809, 1837, 529113195
201548263799736284513/9461, 703, 743, 1113, 1443, 1699, 1757, 2171, 604116131
214587132966923178543/9233, 377, 577, 697, 803, 1483, 1519, 2981, 482913499
227541286933968214571/9117, 371, 387, 679, 959, 1209, 1739, 2279, 265710397
232587496311369478521/9, , 687, 1097, 1199, 1903, 2387, 2651, 328113447
245821746399364712857/997, 173, 479, 1357, 1753, 1847, 1973, 3649, 648117809
258213547699674531284/9131, 209, 357, 649, 1041, 1861, 3201, 4297, 464316389
262539847611674893525/931, 123, 983, 1157, 1399, 1409, 1467, 2381, 616115111
279723851644615832797/9211, 809, 829, 859, 911, 991, 1309, 1579, 487312371
281782495633659428714/9309, 439, 587, , , 2257, 2487, 3323, 337114519
291865439722793456812/9147, 421, 623, 909, 1059, 1199, 1471, 1977, 225710063
306182745933954728169/923, , , 257, 601, 827, 1571, 2069, 22937735
315196482733728469153/91313, 1477, 2063, 2173, 3111, 4493, 4653, 5107, 1041734807
321726584933948562710/9477, 851, 1041, 1799, 2007, 2283, 4077, 4921, 1381931275
338596147322374169582/9113, 187, 841, 1199, 1349, 1727, 1931, 3443, 521316003
341356428799782465315/9349, 443, 731, 743, 1437, 1679, 2081, 2193, 370913365
351582637499473628512/9501, 769, 949, 1099, 1529, 1591, 1749, 2277, 2971
Occurs in twonine.htm 158263749 * 458691723 = 725942717249527 (palindromic)
13435
367142859366395824178/9163, 241, 509, 569, 1091, 1271, 1913, 3671, 4999
Each of these two ninedigitals comes from a sequence of seeds → 36, 1991, ...
14427
372495187633678159420/9117, 1147, 2123, 2343, 2431, 5609, 7299, 12233, 1228745589
387825149633694152873/9299, 733, 1003, 1183, 2187, 2219, 3959, 4493, 1183927915
395482731699613728456/9397, 541, 1541, 1693, 1747, 3259, 4129, 5453, 674325503
405428971633617982451/9359, 667, 1079, 1161, 1169, 2943, 3057, 5593, 847924507
418457162933926175481/9279, 2123, 2211, 2553, 2607, 4703, 4983, 12331, 1637948169
424857319622691375848/9223, 277, 571, 1159, 2663, 3323, 3347, 3373, 775722693
438529647311374692583/999, 627, 1367, 1699, 1793, 2739, 3357, 10099, 1079132571
448256394711749365284/9217, 439, 1399, 2317, 2681, 3023, 3683, 3711, 694724417
454213985677658931245/9137, 701, 1811, 2101, 2327, 2647, 2689, 5467, 616124041
465829641733714692853/91161, 1461, 1763, 1949, 3137, 3219, 4429, 5587, 862331329
478197425633652479180/9529, 1167, 2827, 3267, 3647, 3723, 5577, 6193, 640133331
481645782399328754618/9167, 193, 433, 577, 733, 1201, 2099, 4441, 3016740011
494235791866819753242/9427, 813, 1133, 2123, 2563, 3673, 3771, 6059, 1674737309
504927158366385172942/927, 361, 1479, 3791, 5433, 6547, 8707, 14183, 1744157969
513481562977926518433/91057, 1741, 3019, 3223, 5203, 5389, 6841, 9061, 907344607
525376481299218467352/9203, 949, 1489, 2263, 3183, 4479, 8551, 13457, 1694951523
535792468133186429751/9289, 2187, 3373, 3657, 7539, 9953, 11181, 12813, 1965770649
545782146399364128754/983, 1723, 2287, 2623, 2813, 4063, 6341, 9193, 1735946485
556285973144137958260/9341, 623, 1661, 4199, 6347, 7939, 8957, 11451, 1333354851
565741982633628914754/9151, 939, 1019, 1451, 2093, 2181, 2869, 9421, 1502335147
572417583966938571423/9869, 1373, 1463, 1573, 1759, 2917, 11363, 12661, 2122955207
581579638244283697514/9463, 1163, 1851, 1861, 2117, 4397, 4473, 6579, 700329907
591782563944936528712/91569, 1829, 5139, 6897, 7141, 7451, 8657, 9281, 2084368807
601748259633695284715/9569, 1343, 2141, 3301, 3799, 3847, 4031, 6131, 3124356405
613217685944958671231/91243, 3861, 4141, 5947, 7469, 8073, 11339, 11843, 1309967015
625478613299231687450/91227, 1253, 1313, 1807, 2587, 5697, 9611, 11343, 1557150409
637254861933916845271/9341, 1469, 1681, 2561, 2681, 12199, 12529, 17347, 2115771965
647192685433458629175/979, 2529, 2953, 3389, 3833, 3981, 4659, 11089, 1154944061
654275861933916857241/91329, 3769, 3891, 5367, 6613, 7387, 10659, 20933, 2746787415
665847129366392174857/9367, 1061, 3209, 5959, 7039, 7781, 9341, 12301, 2139768455
675847261399316274852/9549, 759, 2673, 3343, 3411, 5209, 11589, 17347, 1888763767
685419268377386291455/949, 1277, 1589, 2851, 2889, 3023, 3919, 10817, 1712343537
695129487633678492152/913, 589, 889, 2651, 4301, 5687, 6347, 11723, 1247344673
704215698733789651244/9301, 1091, 2701, 4157, 5143, 5689, 5789, 9421, 3625970551
718152347699674325180/9517, 3573, 4551, 5719, 6259, 7923, 10197, 21901, 2383784477
724752938166183925746/92251, 3271, 3989, 6011, 6547, 6557, 8537, 12059, 2274771969
731283745966954738213/92059, 5651, 6039, 6203, 12247, 13447, 20823, 21587, 32161120217
741482596377369528411/91817, 2933, 3199, 4123, 5473, 6239, 17459, 19717, 3666997629
755128736944963782153/9473, 817, 1777, 3923, 6199, 6391, 8327, 8657, 1081347377
762871549366394517823/9681, 833, 1797, 4021, 8409, 10179, 13099, 20807, 45689105515
778472135966953127481/933, 1353, 2343, 2733, 2751, 6329, 7911, 11099, 1801752569
784271586399368517246/9653, 733, 1247, 2839, 3761, 4337, 5149, 5881, 1818142781
795421837966973812450/92483, 4309, 7199, 8323, 12093, 12461, 18117, 23243, 59311147539
804751389266298315741/9309, 2201, 3243, 4047, 4417, 6903, 7289, 7677, 2186357949
811845629733792654812/93283, 5137, 8839, 12923, 18667, 19481, 22799, 25777, 50399167305
829284513677631548291/96349, 6537, 9011, 9819, 14943, 19731, 21959, 26897, 27661142907
835489731266213798450/91923, 5207, 5757, 7909, 8481, 8843, 9731, 11751, 2790787509
849851472633627415895/91003, 1021, 1579, 3559, 5237, 8147, 19021, 24883, 2741391863
855428973611637982450/9363, 2881, 4067, 5391, 9779, 31449, 38071, 49973, 57121199095
869843267155176234890/9779, 4141, 4781, 8071, 9291, 10873, 11531, 23273, 31003103743
874258719633691785243/9781, 1133, 5923, 8377, 10727, 16181, 17551, 39437, 122171222281
882547183699638174521/93573, 4901, 5043, 5317, 6181, 8159, 22543, 43741, 72829172287
898254179366397145283/9159, 2467, 4213, 6143, 8577, 14939, 25769, 49141, 74129185537
901528734966943782517/93277, 3361, 4453, 11807, 15121, 18367, 21319, 22697, 32213132615
915872194633649127850/9713, 2867, 3427, 4811, 11883, 13079, 20961, 25223, 53251136215
921465932788723956412/91883, 2661, 4801, 5937, 8359, 11069, 13719, 16817, 2408789333
931594728366382749512/9883, 937, 2929, 5473, 7183, 8327, 9541, 14053, 2977779103
947159862344326895173/9183, 1473, 1931, 3577, 5373, 9179, 11819, 17477, 2071971731
951523684799748632511/9473, 1819, 2487, 2819, 6941, 8149, 8327, 12749, 2401367777
968256913744731965287/9149, 487, 757, 941, 2729, 4351, 7169, 7559, 1026734409
972657839144193875623/9173, 1639, 5309, 5631, 5747, 17017, 20027, 27999, 31771115313
988265173499437156282/94161, 7099, 8387, 9609, 11009, 17739, 25171, 26391, 35693145259
991254379866897345215/91009, 2119, 5153, 7073, 7843, 12941, 18311, 23909, 31027109385
1002548167399376184521/9119, 489, 3703, 4259, 12817, 13943, 28717, 43277, 90743198067
1011798265433456289711/92817, 3861, 5449, 7009, 7923, 8129, 13189, 15033, 1668780097
1025481723966932718453/92657, 2911, 3961, , , 17099, 17473, 20887, 2332399529
1038254169733796145281/92001, 2523, 5877, 7219, 7711, 12617, 12833, 17461, 33913102155
1042519378466487391523/9523, 877, 1469, 3379, 3913, 3959, 15223, 26063, 89227144633
1051352478699687425313/9469, 913, 1181, 5131, 7567, 8503, 11213, 48587, 57829141393
1062548371699617384523/91919, 3483, 3871, 8979, 13313, 14109, 14551, 18343, 31469110037
1078652174399347125680/9979, 2419, 10593, 11401, 11453, 12441, 14363, 20461, 32857116967
1081875426399362457813/91453, 1763, 2137, 6913, 7897, 10537, 12557, 20047, 39587102891
1091248753699635784213/91303, 9143, 13057, 14819, 18229, 22539, 52789, 53377, 71599256855
1107815463299236451871/91137, 1653, 3353, 9919, 14901, 18211, 20203, 20583, 32437122397
1115247816933961874252/93913, 7039, 8459, 9119, 10781, 17677, 23243, 23927, 44539148697
1125146873299237864153/93711, 7677, 7839, 11353, 11739, 16011, 23917, 26031, 42227150505
1131285643799734658212/91137, 6031, 11817, 19789, 22451, 24623, 24971, 28313, 75031214163
1141475823966932857415/9137, 2039, 4429, 5737, 8711, 25951, 35509, 63523, 97309
Related to ninedigital 974683251 since its decomposition into
ab * cde * fghi (97 * 468 * 3251) returns our initial ninedigital.
Sourceninedig6.htm
243345
1158159476233267495181/9711, 2673, 4149, 6413, 6967, 9117, 11363, 11847, 95557148797
1168251746933964715282/92337, 2923, 7189, 9593, 17849, 20727, 39221, 75209, 95317270365
1172547168399386174524/9923, 3467, 5003, 8861, 10243, 17743, 25817, 43231, 81499196787
1188297145633654179281/92511, 2703, 11207, 17307, 18151, 19279, 28229, 53287, 57907210581
1192541863799736814521/9703, 5463, 7469, 8151, 11097, 19129, 19277, 26399, 35563133251
1205742819366391824755/9463, 4351, 4363, 8629, 10039, 10319, 13007, 19693, 34117104981
1215287139466493178250/93663, 8811, 9267, 14611, 18241, 18733, 29359, 29799, 59411191895
1226172839544593827161/94343, 8241, 9113, 10489, 15199, 18923, 22537, 32493, 43377164715
1234751892633629815742/93377, 3539, 3679, 4367, 17479, 20801, 30319, 38071, 85349206981
1245627813499431872652/94043, 8057, 11079, 11931, 12153, 15247, 15953, 17011, 21107116581
1254126378599587362143/91961, 5247, 5953, 6787, 11143, 14421, 14761, 19213, 67477146963
1266437215899851273464/9787, 1571, 4633, 9307, 10271, 10403, 12737, 24007, 30127103843
1278547192633629174581/91673, 3743, 8613, 11257, 13387, 20119, 20159, 52637, 58399189987
1282184573966937548122/91189, 3387, 12399, 12621, 15361, 24183, 26579, 36169, 110731242619
1292137845966954873121/91279, 2009, 5219, 6193, 9079, 10879, 19397, 35519, 36841126415
1302893457611675439820/92847, 3633, 5123, 12871, 19897, 37193, 48429, 55699, 61249246941
1312568314799741386520/9847, 2409, 4741, 19587, 24079, 28049, 31919, 35741, 118151265523
1322783415699651438725/91271, 3403, 7703, 8467, 12401, 13861, 18881, 26633, 61223153843
1332154387699678345120/93267, 3861, 4343, 12669, 16357, 16617, 17131, 71137, 136411281793
1341857436299263475812/91763, 14571, 15277, 15341, 21311, 31103, 39727, 65349, 130627335069
1351384572699627548311/9763, 1103, 1133, 2891, 9527, 15203, 16907, 34993, 41867124387
1364172398566589327141/92313, 6121, 8859, 13851, 14677, 17719, 18081, 19407, 140489241517
1377951684322348615972/91539, 4283, 4471, 6617, 11473, 20791, 34073, 37829, 41611162687
1387541382699628314577/92417, 3449, 4093, 4393, 7829, 11003, 13939, 36383, 55339138845
1397128435699653482171/91677, 8173, 16683, 21059, 28611, 46231, 50037, 64361, 112321349153
1405167428399382476152/91777, 2493, 4361, 7367, 13193, 14097, 14209, 22157, 116569196223
1417129853466435892172/9367, 11759, 17941, 22373, 26987, 31423, 47641, 51271, 160171369933
1421875463299236457813/91759, 5033, 6639, 7673, 18573, 26483, 29879, 45831, 88097229967
1437182546933964528170/91331, 4631, 7173, 11671, 17353, 37667, 39319, 57733, 64009240887
1442184576399367548126/91051, 4531, 5393, 6361, 8293, 11513, 27187, 66553, 193883324765
1458241673599537614280/92541, 8459, 11097, 12681, 13519, 32629, 34903, 41379, 97361254569
1461379846255264897312/92681, 4903, 6623, 7361, 9331, 12297, 14977, 23173, 54909136255
1471523894766749832511/93269, 4909, 6109, 6589, 7997, 8371, 11603, 30041, 48037126925
1489284531677613548291/91799, 10539, 10761, 13117, 15021, 43739, 44199, 49253, 72453260881
1497829543611634592870/92453, 8593, 13453, 15829, 17953, 30063, 36289, 43549, 76181244363
1508724351699615342784/9593, 2941, 3683, 4297, 6289, 20729, 22199, 32687, 72169165587
1514876925133152967840/97689, 8477, 12469, 13343, 15503, 34307, 41823, 56067, 111133300811
1528425136977963152480/9477, 7851, 16051, 18991, 22791, 25369, 38213, 74501, 84773289017
1539425816733761852493/91307, 5071, 9397, 25289, 26323, 45019, 69737, 79183, 138919400245
1545712893466439821753/94529, 9183, 12051, 14717, 21161, 27091, 30869, 38221, 55963213785
1551569824733742896512/92051, 7711, 19319, 20017, 27853, 40459, 46497, 81651, 83413328971
1565491387266278319453/94913, 6497, 8263, 8881, 10541, 13129, 27551, 36599, 189953306327
1575781249366394218751/92471, 11311, 11873, 21813, 22451, 31117, 40333, 66473, 103081310923
1585269487311378496252/9283, 2451, 11029, 13159, 14733, 14791, 16287, 32981, 33761139475
1592317564988946571321/9451, 2981, 13811, 16027, 16651, 16819, 17071, 27307, 41287152405
1601549832766723894512/93811, 5099, 6849, 21833, 22577, 43057, 46463, 73641, 104087327417
1615714869233296841750/9133, 3641, 19353, 20061, 25399, 36029, 47267, 65307, 72787289977
1628517342699624371586/91483, 6991, 9353, 9929, 20023, 27823, 35389, 57943, 109243278177
1638347125699652174383/914519, 14971, 16831, 19129, 23187, 28413, 29733, 110459, 142303399545
1644728365199156382741/91803, 2999, 8413, 10803, 19649, 28529, 38319, 42087, 95269247871
1657984351266215348970/93263, 5269, 10879, 11401, 32087, 34001, 36233, 36521, 65681235335
1663465172899827156431/92087, 3519, 5681, 6507, 20631, 31519, 44573, 53061, 110123277701
1677241953866835914270/96897, 10483, 13851, 15833, 21571, 33381, 36311, 39283, 77341254951
1685713284699648231755/94021, 5053, 5833, 6311, 9557, 12739, 27091, 27451, 112019210075
1698541769233296714580/95291, 10113, 14761, 21049, 25443, 37433, 68497, 81917, 227557492061
1708943251677615234982/9787, 1421, 9327, 10381, 11581, 41667, 49853, 84739, 108153317909
1711596428733782469511/914003, 15631, 18701, 20447, 28441, 31427, 61427, 77123, 106843374043
1725178423966932487153/92613, 4003, 7123, 21149, 30793, 38301, 62153, 65809, 68503300447
1737861523499432516870/9123, 5841, 8503, 11979, 19939, 34723, 65263, 74943, 111761333075
1745812649377394621857/91513, 1873, 1979, 13187, 13613, 24023, 26371, 67741, 95833246133
1754581972633627918540/92599, 14837, 15677, 16861, 19133, 35409, 67881, 120931, 166763460091
1761623495877859432612/96861, 13793, 20443, 23269, 23319, 39329, 42781, 46329, 154697370821
1775932786144168723951/98887, 9449, 25003, 28589, 29627, 47377, 53669, 55033, 68167325801
1789528614733741682592/9449, 3131, 8589, 16683, 33523, 38553, 41013, 97687, 105047344675
1794257981366318975241/91013, 2673, 5467, 12947, 18491, 28651, 59459, 133489, 171347433537
1805287149633694178258/9467, 673, 5227, 8221, 16831, 34487, 39059, 58603, 116927280495
1815487216933961278450/9561, 10407, 11133, 16203, 17193, 18357, 19499, 149347, 167387410087
1825814267933976241851/961, 1149, 8357, 11219, 18163, 22463, 37481, 38443, 127729265065
1835412783699638721452/95447, 9427, 10637, 12341, 58553, 64871, 100489, 114719, 155671532155
1845419728366382791450/9447, 6109, 11961, 14749, 15283, 27711, 33929, 62681, 78841251711
1851275943866834957210/91961, 7711, 14103, 14353, 25267, 37563, 60929, 71539, 174691408117
1861489675233257698413/9961, 4141, 9517, 19039, 19709, 32237, 42571, 46363, 49243223781
1874281576399367518242/9141, 14693, 22847, 30033, 55721, 56793, 70121, 71279, 81433403061
1882814357699675341820/99183, 9507, 13479, 26327, 35621, 42963, 114657, 164807, 187057
Occurs in twonine.htm 268749153 * 281435769 = 75635624542653657 (palindromic)
603601
1898135792466429753180/92761, 3479, 5621, 12257, 15719, 23881, 24649, 52913, 143869285149
1902184375699657348122/94649, 9217, 10787, 16009, 16393, 23343, 23723, 43973, 44747192841
1915213874966947831251/92643, 3033, 4911, 9053, 16851, 21491, 22467, 27247, 33551141247
1925821436799763412853/92297, 5063, 6847, 15949, 34291, 69259, 94751, 135997, 333071697525
1931782459633695428712/95949, 15667, 15999, 21983, 33451, 51209, 56779, 96407, 262663560107
1944521936877863912541/91173, 1209, 1983, 30593, 34879, 38591, 53029, 57307, 83871302635
1955381492766729418350/94963, 8591, 20917, 22337, 22561, 44693, 50113, 100661, 358369633205
1965497812633621879450/96419, 22903, 43327, 44841, 48099, 56607, 58577, 70307, 451811802891
1978214536799763541280/913123, 15747, 19041, 20949, 36487, 102377, 107701, 125367, 125689566481
1981546287933978264514/99041, 20827, 33697, 36451, 45443, 64349, 71641, 102181, 203809587439
1997412568399386521470/91641, 6031, 29427, 39413, 43821, 48169, 58731, 95711, 312301635245
2004581723966932718542/97157, 8707, 10887, 16457, 36681, 62419, 70079, 79121, 133259424767
2015123479866897432151/95299, 6457, 22217, 26989, 45109, 60923, 93737, 114301, 143209518241
2025291478366387419250/9299, 2217, 3737, 3937, 5109, 32259, 62363, 157979, 187331455231
2032749185366358194721/9217, 2609, 3113, 9691, 15063, 16051, 22773, 77209, 148357295083
2042941857633675814925/917, 691, 961, 5063, 12799, 13037, 73729, 90451, 96557293305
2057581492633629418571/93729, 7997, 12323, 14469, 20437, 26969, 30953, 79117, 341671537665
2061528436799763482510/94469, 17157, 24613, 34017, 39879, 41671, 116693, 136977, 282251697727
2071285347699674358213/91879, 4613, 4639, 17699, 39377, 45551, 61979, 79321, 86713341771
2085493182766728139453/92417, 5551, 5579, 9377, 10851, 56289, 69291, 134569, 287239581163
2094157823699632875140/910197, 10577, 13081, 15521, 22143, 26583, 39787, 76571, 95491309951
2109238576144167583294/95491, 6583, 9787, 24463, 40727, 64621, 65423, 72109, 107483396687
2119548312677621384590/918227, 20931, 22671, 32571, 51101, 58299, 60797, 82441, 182361529399
2128564271933917246581/96229, 10053, 30751, 41991, 53761, 59429, 61557, 176057, 205037644865
2134591287366378219541/91991, 10769, 15889, 26639, 45947, 50339, 94193, 256421, 360041862229
2144852719366391725840/99423, 17141, 20993, 23513, 26121, 39183, 64051, 96109, 195101491635
2152584169377396148520/93513, 5811, 9361, 27627, 30921, 44659, 85283, 88393, 136191431759
2165431287699678213453/9811, 6493, 13807, 17051, 19879, 27361, 55873, 117419, 253129511823
2177148526933962584170/91369, 7051, 30459, 36053, 37683, 67331, 70807, 73139, 105247429139
2181437528966982573412/910451, 23613, 40483, 51377, 61671, 67113, 68947, 166201, 295127784983
2194872315966951327841/98123, 14267, 14729, 18491, 74969, 105479, 117161, 138941, 144727636887
2202561487933978416521/913283, 18309, 26971, 31483, 38427, 71267, 128649, 156389, 5660571050835
2215267148933984176250/99339, 12259, 24299, 27863, 33627, 54653, 73753, 126503, 148621510917
2225231498766789413253/94241, 10201, 27701, 27961, 45379, 55801, 61069, 78961, 87863399177
2234972581366318527941/95379, 6203, 8961, 16169, 19749, 48389, 64053, 71003, 169103409009
2247384512699621548373/99893, 19451, 24637, 29339, 31219, 43011, 49903, 71473, 160613439539
2252478516933961587423/910789, 12509, 15763, 33869, 39193, 46589, 74897, 80201, 327107640917
2265243168799786134252/96881, 16539, 24193, 27107, 45871, 68473, 83133, 120201, 199619592017
2278563214799741236580/93133, 19513, 28523, 30239, 32431, 40623, 89727, 117381, 131173492743
2286521873499437812563/91411, 12667, 16591, 17293, 20497, 38557, 49003, 63221, 130187349427
2298254716933961745280/98553, 24761, 33047, 35079, 38709, 63139, 123473, 315403, 4882671130431
2308254179633697145280/9553, 4761, 10807, 15353, 15687, 52257, 102137, 105077, 131389438021
2311492537688673529410/95687, 7921, 12793, 20591, 24289, 27137, 33011, 57629, 115247304305
2325629473811837492651/922607, 31103, 35499, 35737, 38383, 48651, 59557, 61833, 73767407137
2334962781533518726940/96879, 12001, 14509, 29973, 43353, 47763, 53559, 80601, 136609425247
2344218957366375981246/91657, 9973, 10559, 15661, 50663, 71549, 84467, 99773, 119641463943
2354829561377316592841/92947, 18183, 18893, 39149, 48411, 54637, 87307, 221201, 221397712125
2364579821633612897540/916779, 21349, 25923, 48167, 50421, 71029, 118221, 208523, 365953926365
2378142536799763524180/914917, 18221, 27521, 64511, 65351, 65953, 87571, 95051, 346181785277
2381427853699635872411/98221, 19923, 21033, 24559, 41313, 55181, 60701, 138649, 273413642993
2392548167933976184521/91033, 5181, 5357, 8239, 10857, 22033, 36171, 155881, 214819459571
2405842179633697124858/9181, 239, 3229, 6581, 25673, 164707, 201497, 250981, 3991071052195
2415827143966934172850/911517, 24581, 25991, 59191, 65241, 87153, 107263, 154319, 263219798475
2422873145699654137822/95991, 14979, 15947, 17053, 25337, 26393, 84679, 152773, 204943548095
2433481759622695718434/96889, 8887, 21739, 27841, 42839, 63329, 77429, 107773, 119999476725
2445169248733784296152/912869, 21817, 33983, 44273, 46677, 54267, 55169, 57733, 197129523917
2458294165733756149280/96237, 13783, 15577, 18117, 23939, 41899, 83931, 91883, 418891714257
2466184257933975248164/910643, 11789, 16409, 42479, 49303, 57719, 80329, 116821, 232439617931
2474518326799762381541/92479, 19877, 21703, 41831, 55493, 76329, 83611, 111409412732
2484512986377368921542/97787, 8127, 30291, 35449, 50189, 65881, 75469, 77707, 139781490681
2498425167399376152482/911809, 23947, 25993, 36527, 48521, 92777, 131293, 268829, 269071908767
2502718549633694581723/95993, 21787, 28323, 29037, 49233, 49953, 53777, 73897, 181673493673
2518547213966931274581/95001, 6721, 9953, 12177, 24223, 39257, 73711, 93313, 105853370209
2529846175233257164898/93313, 5657, 10663, 14867, 27919, 33557, 59779, 85751, 132283373789
2535428179633697182450/910997, 12733, 27057, 33993, 68793, 69199, 150293, 166463, 220979760507
2545268714399341786253/92701, 7057, 11783, 42513, 65441, 92921, 132479, 143129, 191347689371
2555182437966973428150/96497, 23573, 27709, 47377, 48499, 52547, 81419, 109079, 201091597791
2564537281699618273544/98499, 9989, 11483, 14731, 27833, 33921, 36433, 103999, 364223611111
2575241398766789314250/94161, 7833, 10263, 17999, 21853, 25751, 111621, 194073, 357181750735
2582157438699683475124/97247, 7999, 13451, 20203, 28603, 49723, 67391, 128243, 155021477881
2592143685977958634121/912111, 28083, 39633, 43969, 88517, 110283, 211799, 221881, 222057978333
2604712856933965821741/914271, 19191, 31661, 36799, 64039, 89817, 102613, 117427, 293857769675
2615126478933987462151/910373, 11851, 39941, 50809, 79343, 86669, 86873, 104753, 155747626359
2621842573966937524812/91851, 6873, 14149, 20099, 21599, 25887, 45059, 186199, 242599564315
2631265379844897356210/9851, 11913, 16291, 22759, 24167, 27819, 36949, 54243, 102903
Related to ninedigital 376854921 since its decomposition into
a * bcd * efghi (3 * 768 * 54921) returns our initial ninedigital.
Source → (J. Heynderickx)
297895
2647245831966913854274/921457, 23201, 31819, 38837, 51049, 64969, 80449, 125479, 283519720779
2658245371699617354281/913679, 25179, 48411, 49383, 71533, 102619, 114171, 189343, 240031854349
2668241753966935714281/94887, 5179, 8411, 14171, 37113, 78747, 83713, 100091, 145733478045
2678124735699653742181/91903, 4171, 5521, 14063, 27401, 50017, 103961, 137929, 182831527797
2682815743699634751821/97929, 11013, 16017, 22139, 47769, 72069, 92821, 109543, 114589493889
2692148759366395784120/95853, 6017, 11847, 12529, 34311, 69553, 99649, 164021, 222629626409
2709137682544528673196/99649, 28403, 31111, 38113, 38957, 57773, 68917, 71527, 79567424017
2713851492677629415830/91111, 25179, 25857, 40953, 48771, 78529, 88319, 147961, 228339685019
2724682157399375128640/98771, 23479, 31083, 38689, 44229, 83803, 306101, 462943, 4923731491471
2734852176933967125840/97403, 11143, 18851, 23947, 29029, 65021, 67177, 107237, 401093
Occurs in twonine.htm 163874529 * 485217693 = 79514820902841597 (palindromic)
730901
2742648571399317584622/93947, 7177, 19669, 25319, 60389, 162763, 212049, 281311, 3258111098435
2752579648133184697522/98481, 18931, 20891, 37741, 47003, 75339, 92739, 103511, 140587545223
2765318247699674281356/911621, 12323, 17623, 19633, 30241, 31439, 36697, 84629, 199883444089
2773549182766728194531/912881, 13061, 24453, 70363, 82327, 90387, 116847, 146833, 162967720119
2789671584233248517691/92323, 16177, 36759, 44859, 60129, 76849, 79457, 119029, 174259609841
2792518493766739481520/911381, 13057, 15367, 16027, 82489, 103961, 126071, 148621, 455323972297
2801248957633675984211/95367, 14709, 27471, 30753, 45571, 49461, 72981, 73697, 180419500429
2817584162933926148571/92981, 3289, 6303, 19403, 25839, 35299, 62667, 77227, 144463377471
2824256183799738165242/91717, 21547, 38741, 75851, 83177, 85489, 135869, 163979, 243937850307
2832814795633659741820/91547, 5489, 14509, 16021, 52767, 61621, 71621, 190619, 214511628705
2841975824633642857912/94509, 4589, 13767, 41761, 91737, 108609, 138257, 381157, 7885371572923
2851524387699678342515/99199, 39733, 85427, 95027, 105809, 134537, 164419, 327481, 8269691788601
2866198253477435289161/916121, 22239, 27421, 29439, 31341, 43697, 44233, 56209, 127989398689
2878524179366397142581/98191, 13893, 14023, 14837, 47153, 55187, 116149, 134521, 318263722217
2884572819633691827546/91217, 10939, 16001, 31139, 37699, 58637, 71531, 109477, 179099515739
2894581276399367218541/93523, 18701, 34529, 38221, 56969, 82563, 190279, 328009, 3412091094003
2906473182599528137462/910577, 19617, 26627, 28009, 32253, 64809, 81787, 121503, 294989680171
2918514237966973241581/97007, 13967, 19019, 38137, 97567, 103081, 112811, 129217, 267443788249
2928125473699637452182/94707, 9019, 13961, 30903, 37407, 139597, 174281, 342589, 3763011128765
2934135827966972853140/923903, 24849, 31493, 35347, 50517, 72853, 138129, 241439, 5923391210869
2943487521966912578438/91493, 16207, 16339, 17627, 20183, 49549, 74779, 81409, 295663573249
2955318264977946281351/959037, 65923, 95623, 98187, 110567, 121573, 168657, 249007, 3351431303717
2965124869733796842152/99037, 30999, 35719, 50307, 61971, 76757, 133649, 210687, 360731969857
2978471532699623517483/91793, 22093, 25289, 45767, 51863, 60731, 71621, 209099, 314903803159
2985814297366379241850/91863, 8067, 16623, 20673, 22233, 76811, 83973, 200219, 312649743111
2992174698533589647121/92233, 6623, 13949, 18513, 57577, 57893, 75943, 83739, 109517425987
3002457683911938675427/9233, 12653, 39209, 52543, 76907, 98249, 127289, 127327, 137147671557
3014231985766758913242/98151, 11423, 27293, 47757, 48763, 55443, 134741, 211453, 316909861933
3021594278366387249510/913443, 28561, 36991, 47007, 57147, 62829, 82177, 197821, 206053732029
3038147259633695274180/92177, 3443, 7007, 28523, 38927, 81301, 98153, 253121, 412643925295
3048972415366351427980/96639, 8153, 13273, 16227, 53211, 62041, 116837, 272291, 308357857029
3051452387966978325411/912539, 20423, 24771, 31117, 49687, 113443, 170951, 245933, 343441
Occurs in twonine.htm 145238796 * 465923781 = 67670208980207676 (palindromic)
1012305
3064271589366398517245/91763, 22259, 32387, 41779, 52057, 53303, 97117, 110921, 134909546495
3078641523799732514681/912023, 61169, 76617, 83223, 114633, 123453, 138281, 151191, 3601731120763
3088642195733759124683/922531, 26153, 38061, 48457, 63677, 85411, 112641, 113331, 125089635351
3094715628933982651740/910367, 23153, 50219, 56971, 60049, 151081, 173437, 198517, 264517988311
3105468291733719286451/96971, 13897, 19487, 31017, 36423, 64799, 113827, 131289, 372281789991
3114158732699623785141/92883, 13827, 16357, 24673, 31139, 72281, 192649, 234179, 4185071006495
3121482597633679528416/93827, 10289, 24923, 60689, 78083, 167191, 178637, 266381, 3598511149871
3134218597366379581240/911989, 14861, 17853, 45059, 82079, 95161, 127929, 267487, 311443973861
3149812457366375421891/95161, 7197, 7853, 18141, 20609, 34149, 52403, 260477, 290977696967
3155429718633681792452/99199, 20953, 74899, 127369, 133057, 154649, 168949, 190817, 3408011220693
3167524813699631842571/913801, 13851, 16667, 44031, 47403, 54649, 110591, 207661, 441707950361
3174159726833862795140/94031, 13869, 23991, 58127, 61053, 73947, 148771, 169641, 6629811216411
3181548726399362784514/93869, 10081, 16879, 33911, 57559, 111263, 215231, 233411, 7539531436157
3192647598133189574621/911139, 19547, 46981, 83929, 99033, 100837, 104543, 166699, 6818571314565
3204578126399362187540/96981, 21127, 22103, 34713, 66699, 122769, 187991, 282401, 3390771083861
3211453782699628735412/945287, 70301, 81499, 86021, 90283, 95791, 105601, 194651, 2866271056061
3221598247366374289513/919009, 20201, 29927, 30027, 43739, 75961, 85807, 527359, 8535611685591
3238452716399361725481/911671, 19949, 39201, 41551, 51249, 66759, 225049, 265309, 6889911409729
3244182569733796528145/911437, 16963, 34369, 37501, 77687, 96641, 137051, 197377, 226361835387
3258491572366327519482/98511, 25969, 34529, 67551, 78231, 98827, 125171, 199457, 6500891288335
3268724659311395642780/9511, 24141, 26677, 32937, 50089, 51243, 91001, 100933, 131619509151
3279572461833816427592/91001, 1243, 4817, 6677, 7127, 14971, 31619, 57233, 355003479691
3288143526799762534182/912833, 13069, 41451, 55003, 64901, 78083, 105209, 169629, 187897728075
3294169875322357896142/91451, 3069, 13937, 31723, 62557, 69267, 75999, 112717, 126657497377
3307431582699628513475/94273, 7663, 17977, 20593, 61337, 67031, 92567, 222953, 388841883235
3315287914633641978250/924723, 31097, 32543, 35347, 43417, 70411, 106611, 138137, 218779701065
3324786152933925168743/934379, 42701, 43981, 82129, 118977, 147439, 219151, 241973, 3644931295223
3334812537966973521841/911971, 17233, 18977, 19151, 50611, 64493, 148811, 212003, 331199874449
3341542973866837924511/98977, 15453, 18661, 33351, 51223, 59529, 77179, 85379, 255227604979
3358562374199147326580/95379, 10351, 20581, 45453, 47971, 49797, 56217, 243419, 450583929751
3368246713599531764286/99637, 12071, 39499, 44237, 122027, 134279, 161521, 176797, 276047976115
3372183746599564738120/95489, 34279, 87363, 144331, 149853, 192049, 206107, 359843, 4606031639917
3388952147366374125980/97363, 93421, 112753, 119857, 129317, 147087, 165507, 205309, 2915271272141
3399812753466435721890/93421, 10439, 29317, 97031, 105193, 108143, 147631, 201487, 230219932881
3404158392677629385142/940369, 42351, 43319, 51147, 53837, 101551, 133637, 162889, 219531848631
3418527416399361472580/96697, 12681, 16461, 80399, 89661, 127119, 168421, 412093, 5304971444029
3421847256933965274815/927119, 40973, 53579, 81869, 87683, 99691, 273971, 450881, 4901571605923
3431459287633678295410/9, , 72083, 115313, 139887, 145497, 269467, 270853, 3451031386385
3441254389766798345214/94091, 20377, 28099, 41057, 45103, 56193, 66053, 143411, 186763591147
3459517284366348271591/913123, 24473, 27671, 49489, 80047, 103327, 123683, 213389, 265727900929
3465832147966974123851/912039, 13769, 15403, 28217, 66103, 116023, 147789, 373639, 3820571155039
3472785941366314958721/98217, 28611, 58609, 70213, 83143, 94319, 114033, 173723, 4627731093641
3483142586799768524134/913379, 14033, 14947, 70391, 74651, 81959, 135349, 202087, 4199711026767
3498435721966912753481/91959, 8949, 24761, 28083, 56529, 62057, 65433, 93277, 541673882721
3509562147833874126591/93277, 16513, 20983, 33507, 73409, 92759, 93243, 142849, 8953971371937
3512618573944937581621/922183, 24211, 27769, 28837, 32879, 51389, 134849, 218933, 268631809681
3522861394577549316822/92183, 9903, 10753, 18129, 32497, 48827, 55587, 73001, 272793523673
3532175394866849357121/9183, 8129, 10373, 71907, 77017, 87769, 108431, 140101, 273439777349
3542418975366357981422/96191, 12731, 21971, 22747, 24341, 37439, 47987, 57731, 333107564245
3554162835977953826141/918777, 47281, 60437, 81009, 87807, 100379, 121847, 133661, 5161531167351
3568945712366321754982/97807, 22547, 34071, 50539, 70589, 105093, 175849, 175931, 232897875323
3574872156399365127840/99889, 14801, 14803, 16027, 20027, 32903, 169741, 232177, 349921860289
3581584279633697248512/910893, 21279, 41853, 92787, 158189, 174123, 202999, 272167, 4115511385841
3594198236755763289140/911729, 23991, 38951, 80157, 116919, 119717, 134057, 168671, 172579866771
3607821549633694512875/932051, 32233, 38881, 46223, 46271, 47279, 85721, 90437, 119303538399
3611246785933958764210/912183, 32483, 80127, 116587, 126643, 140679, 271073, 288277, 3996191467671
3621623549877894532612/92183, 22417, 24913, 99619, 107443, 125891, 137849, 157863, 220859899037
3632574813966931847523/94913, 32483, 91393, 91751, 113861, 155251, 246271, 327943, 4604271524293
3642675149833894157621/910221, 36361, 38883, 51467, 58813, 74859, 93949, 151199, 441779957531
3655784216399361248750/91467, 23991, 25003, 35651, 66363, 101013, 172451, 215303, 3649731006215
3662138465799756483125/916381, 17189, 17867, 25957, 28789, 40387, 54829, 55651, 141341398391
3675247813966931874252/94991, 10313, 52341, 58509, 66839, 126049, 161443, 185789, 211013877287
3685214897633679841254/92829, 10177, 26049, 96551, 146683, 292811, 314723, 320831, 4609191671573
3692194763855836749121/97403, 11603, 24221, 67223, 117949, 117953, 132077, 150311, 296941925681
3701482376955967328411/91603, 40279, 41631, 46719, 64111, 76303, 103603, 112037, 274929761215
3711427358699685372411/9603, 10073, 16207, 23771, 34981, 73203, 112167, 170203, 8550731296281
3723857216499461275836/99391, 10139, 10631, 18443, 45937, 91757, 118123, 160513, 516199981133
3738542791366319724580/95357, 11853, 12913, 55347, 113047, 140371, 174333, 295889, 3070431116153
3742857419366391475822/919263, 21073, 28077, 47241, 49727, 74333, 90979, 244109, 245573820375
3751574283699638247510/928193, 28721, 52151, 62293, 63893, 158213, 159083, 392231, 5637171508495
3764813725699652731846/931233, 45341, 52579, 53623, 79291, 81749, 82373, 96971, 292921816081
3777251934866843915270/99291, 66979, 92521, 107673, 134819, 214687, 237731, 296647, 3010631461411
3785847931266213974855/911411, 39229, 59407, 70361, 87751, 101989, 105311, 140963, 174467790889
3792849351766715394820/916929, 21549, 49489, 68783, 116479, 125829, 145629, 208857, 3174491070993
3804589127366372198542/99489, 10221, 18213, 32921, 45629, 65089, 90851, 370147, 6847331327293
3819854261733716245891/94147, 16571, 47003, 50611, 54989, 84733, 130603, 207419, 305143901219
3822861459733795416820/925797, 26243, 27341, 30603, 38763, 73023, 150361, 212749, 6240711208951
3832485713966931758421/95797, 13047, 16647, 28179, 39107, 135383, 186329, 196757, 8774811498727
3842851734966943715824/91531, 12977, 16747, 35383, 37847, 59909, 69701, 290743, 374819899657
3851947826533562874910/913431, 31361, 38929, 95623, 131373, 141873, 161821, 199001, 3688191182231
3861582367499476328511/93431, 10059, 39109, 51097, 68819, 105931, 176829, 251793, 290567997635
3875281679433497618251/911539, 11627, 35749, 48353, 93511, 111793, 165943, 168773, 10635131710801
3882158743966934785121/98303, 21793, 117189, 119967, 126171, 310471, 408779, 449797, 5508192113289
3898514972633627941581/941961, 49761, 74261, 126737, 139249, 155139, 168559, 263087, 3908631409617
3907142835966953824174/913207, 19493, 22301, 24257, 63599, 90863, 107647, 151351, 276721769439
3912417859366395871421/94257, 8001, 9493, 33219, 184983, 308517, 308539, 397283, 5441591798451
3928672543199134527682/910843, 23909, 27177, 38029, 60609, 91863, 128903, 161373, 451871994577
3931256843799734865212/961373, 82531, 95107, 100597, 122177, 198679, 239173, 287249, 3132911500177
3945341298766789214350/935817, 36281, 39741, 55749, 104193, 140131, 151823, 265387, 317993
Related to ninedigital 938526741 since its decomposition into
ab * cde * fghi (93 * 852 * 6741) returns our initial ninedigital.
Sourceninedig6.htm
1147115
3953174852699625847131/96281, 19943, 21929, 31323, 42559, 44149, 66513, 152933, 238513624143
3961425869733796852417/99943, 10883, 20483, 22877, 35153, 50887, 54371, 67261, 68909340767
3978145279633697254180/95511, 65307, 88581, 105131, 138347, 139207, 218449, 382447, 11241892267169
3987425869311396852473/911447, 16509, 24697, 42421, 71617, 145843, 145873, 214031, 5088591181297
3996748153922935184761/924673, 30613, 34079, 74861, 114763, 253099, 293377, 300443, 3373211463229
4008915463722736451982/912513, 14639, 14763, 19761, 37003, 69713, 93173, 133863, 273467668895
kndnd'/9sequencesum
4504561827933972816546/98279, 13963, 16309, 36653, 40763, 121603, 139133, 204371, 337031918105
4785712483966938421751/91337, 10209, 41427, 58137, 104229, 142631, 235397, 356369, 7832931733029
5009874261533516247892/915431, 38899, 56921, 71583, 110169, 241961, 249699, 429973, 5547491769385
5502187594633649578121/921287, 30339, 46241, 49573, 60633, 144157, 224833, 284113, 3081071169283
6004285317699671358246/99181, 129457, 133213, 173051, 188911, 189661, 293977, 303671, 5981932019315
6508491352766725319483/930313, 40781, 49679, 91101, 100097, 101097, 103387, 226901, 4798691223225
6667534821699612843574/92557, 67237, 148739, 181751, 249239, 286543, 302257, 1119817, 17032794061419
7005182476399367428152/926031, 86851, 135813, 175121, 245901, 434361, 791473, 866467, 15177194279737
7404281579366397518241/93087, 188461, 193669, 225363, 368763, 662031, 834187, 859361, 12253514560273
7503871546299264517830/974033, 87467, 120751, 144913, 187799, 358321, 364501, 374911, 24198774132573
8005824196733769142852/916593, 29323, 75297, 93999, 153339, 292877, 450617, 964109, 12855473361701
8508431972566527913481/943433, 83241, 145747, 157687, 173417, 189127, 265347, 306521, 6962512060771
9001328754699645782313/928447, 79753, 88717, 175477, 278491, 298289, 884231, 1176401, 23565615366367
9114786123599532168740/918453, 107943, 109593, 214577, 214599, 331939, 680911, 1098537, 22042574980809
9565874612933921647850/95341, 8341, 8441, 53079, 62629, 83657, 418479, 980873, 12109272831767
9872718495366359481721/920119, 76549, 87901, 164617, 195289, 809831, 826969, 908357, 40697477159379
9999681275344357218690/937829, 62257, 68387, 110231, 173327, 296879, 326953, 509377, 6474712232711
10006127584399348572161/92257, 10231, 57653, 134941, 171033, 196839, 229107, 1295671, 43433816441113
10015124837699673842152/963957, 124971, 278667, 325083, 389787, 495737, 794579, 1840231, 18900976203109
11002148593766739584120/9114957, 134939, 201593, 208707, 297787, 729313, 744961, 800969, 12768534510079
11111897425366352479810/944187, 75713, 141493, 345301, 370437, 768867, 1324461, 1473007, 24897477033213
12004651892377329815646/9122537, 129959, 181201, 270913, 307859, 392867, 423961, 1307639, 13223174459253
12345128479366397482152/959009, 288931, 361227, 410159, 478261, 1525003, 1871429, 3065153, 419983912259011
13024851672399327615842/950159, 62917, 105881, 178847, 427751, 553381, 813941, 929651, 14612274583755
13007815249633694251872/96087, 33657, 51459, 291429, 1115589, 1138639, 4305431, 5384869, 549910117826261
14004873219655691237840/971297, 142783, 154149, 255263, 463659, 1268961, 1551823, 1876001, 24356078219543
14416481925733752918460/910901, 242011, 339141, 341407, 675521, 686589, 804111, 2209933, 6698923
A palindromic seed (1441) that needs a palindromic k (10901) with d=6
Occurs in twonine.htm 173542986 * 375291846 = 65129267576292156 (palindromic)
Related to ninedigital 396427518 since its decomposition into
a * b * cdefghi (3 * 9 * 6427518) returns our initial ninedigital.
Source → (J. Heynderickx)
12008537
15006785129433492158763/977501, 139327, 251639, 266327, 458951, 468667, 538859, 1210711, 35317516943733
16007418529633692581470/9
2523, 74463, 76059, 82607, 236517, 301047, 589459, 1512529, 5632487
[789] the ninedigital represents the layout of
[456] a numerical keyboard from top to bottom
[123] and from left to right
8507691
17001745268933986254711/95169, 112029, 324153, 356703, 874641, 930781, 987537, 3942893, 605268713586593
18002598641377314689524/9200561, 384049, 432599, 493111, 968819, 1111697, 1467847, 1649981, 18812278589891
19005847213699631274850/9336309, 482489, 556387, 804303, 1022441, 1073293, 1297673, 3965377, 556033315098605
19564718652399325681742/936733, 42761, 338029, 354901, 616489, 803183, 993859, 1444321, 10921759
record k with d=9 10921759
15552035
19917142859366395824170/932901, 286187, 348821, 536151, 545259, 1161639, 1789579, 2766379, 6512957
Each of these two ninedigitals comes from a sequence of seeds → 36, 1991, ...
13979873
20008529416733761492580/972187, 72583, 164349, 178763, 372071, 1386941, 1646827, 1763879, 535192111009521
20232184759633695748120/9437349, 770407, 899151, 1017813, 1189353, 1961333, 5137583, 9390491, 980609330609573
20248174529366392547181/999151, 107373, 264921, 320217, 377163, 855589, 1156351, 1990387, 516621110337363
22225982647133174628951/9180079, 331289, 642283, 735469, 1161727, 1652853, 2588043, 3227151, 10858933
record k with d=3 10858933
21377827
33332548913766731984520/9283619, 399841, 557293, 911407, 2097161, 2489663, 3731563, 5981041, 1731357133765159
```
\\ This is my PARI/GP program code for WONplate 225 by PDG [June 9, 2023] → seq225.gp
{
seed=40;
m=matrix(9,2);
sumk=0;
for(d=1, 9,
for(a=seed, seed,
b=1;
until(flag==0,
f=(d*(10^a-1)/9)*10^(#(digits(b)))+b;
while(ispseudoprime(f)==0,
b+=2; f=(d*(10^a-1)/9)*10^(#(digits(b)))+b;
);
ad=0; flag=0;
for(i=1, a-1,
ad++; fd=(d*(10^ad-1)/9)*10^(#(digits(b)))+b;
if(ispseudoprime(fd), flag++; break(); );
);
b+=2;
);
k=b-2; m[d,1]=k; m[d,2]=d; sumk+=k;
print("[",d,"^^",a,"][",k,"]");
b=1;
);
);
v=vecsort([m[1,1],1; m[2,1],2; m[3,1],3; m[4,1],4; m[5,1],5; m[6,1],6; m[7,1],7; m[8,1],8; m[9,1],9]~);
print(v);
print("Seed ",seed," yield ninedigital ",v[2,1],v[2,2],v[2,3],v[2,4],v[2,5],v[2,6],v[2,7],v[2,8],v[2,9]);
print("Sum of k's = ",sumk);
cnt=0; print1("{ "); for(i=1,9, if(isprime(v[1,i]),cnt++; print1(v[1,i]," "))); print1("} ");
print("Primescore is ",cnt,"/9");
}

```
 A000225 Prime Curios! Prime Puzzle Wikipedia 225 Le nombre 225
```

```

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Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com