COMMENT ā VALID 00004 PAGES
C REC PAGE DESCRIPTION
C00001 00001
C00002 00002 PALINDROME FORMATION TESTED TO A MAXIMUM OF 100 DIGITS
C00018 00003 A list of all 2-digit and 3-digit numbers that require more than 10
C00023 00004 Attempt at a palindrome production with the number 196 by the special scheme of
C00045 ENDMK
Cā;
PALINDROME FORMATION TESTED TO A MAXIMUM OF 100 DIGITS
DATA FOR 2-DIGIT DECIMAL NUMBERS
24 MAX ADDS FOR 90 PALINDROMES, WITH 0 INTRANSIGENT CASES
PALINDROMES FOUND
FOUND #ADDS FOUND #ADDS FOUND #ADDS FOUND #ADDS
9 0 49 1 20 2 4 3
4 4 2 6 2 24
NO INTRANSIGENT CASES
DATA FOR 3-DIGIT DECIMAL NUMBERS
23 MAX ADDS FOR 887 PALINDROMES, WITH 13 INTRANSIGENT CASES
PALINDROMES FOUND
FOUND #ADDS FOUND #ADDS FOUND #ADDS FOUND #ADDS
90 0 213 1 281 2 145 3
63 4 31 5 9 6 17 7
7 8 2 10 7 11 2 14
7 15 4 17 2 22 7 23
INTRANSIGENT CASES TO 223 ADDITIONS AND 100 DIGITS
SUM1 MID# # CASES
7 9 7
15 8 4
17 7 2
DATA FOR 4-DIGIT DECIMAL NUMBERS
21 MAX ADDS FOR 8767 PALINDROMES, WITH 233 INTRANSIGENT CASES
PALINDROMES FOUND
FOUND #ADDS FOUND #ADDS FOUND #ADDS FOUND #ADDS
90 0 2527 1 2528 2 1192 3
829 4 384 5 388 6 227 7
50 8 63 9 10 10 42 11
110 12 67 13 1 14 75 15
58 16 9 17 27 18 26 20
64 21
INTRANSIGENT CASES TO 219 ADDITIONS AND 100 DIGITS
SUM1 SUM2 # CASES
6 13 36
8 13 48
8 18 7
13 7 48
13 16 18
16 5 18
16 14 14
17 7 16
17 8 18
17 16 6
17 17 4
DATA FOR 5-DIGIT DECIMAL NUMBERS
55 MAX ADDS FOR 84226 PALINDROMES, WITH 5774 INTRANSIGENT CASES
PALINDROMES FOUND
FOUND #ADDS FOUND #ADDS FOUND #ADDS FOUND #ADDS
900 0 12347 1 21386 2 15524 3
7840 4 5504 5 4107 6 2538 7
2344 8 1674 9 1914 10 1567 11
1231 12 777 13 540 14 458 15
341 16 271 17 303 18 354 19
254 20 298 21 103 22 153 23
148 24 199 25 106 26 53 27
60 28 178 29 155 30 83 31
11 32 88 33 22 37 161 38
77 39 9 40 32 47 32 52
64 53 16 54 4 55
INTRANSIGENT CASES TO 211 ADDITIONS AND 100 DIGITS
SUM1 SUM2 MID# # CASES
9 3 5 36
4 5 5 24
4 6 5 27
8 7 5 64
4 8 5 35
6 8 5 53
9 3 6 36
4 5 6 24
4 6 6 27
9 6 6 63
8 9 6 80
6 1 7 12
9 2 7 27
6 3 7 24
7 4 7 35
9 4 7 45
4 8 7 35
6 8 7 53
8 8 7 71
9 8 7 81
2 2 8 5
4 4 8 19
8 7 8 64
4 8 8 35
4 3 9 16
4 6 9 27
6 6 9 41
10 6 9 62
8 7 9 64
4 8 9 35
6 8 9 53
9 10 8 81
8 11 0 64
8 11 2 64
4 11 3 32
4 11 7 32
8 11 7 64
9 11 8 72
8 12 0 55
8 12 1 55
3 12 3 21
4 12 3 27
8 12 3 55
7 12 5 49
8 12 5 55
5 12 6 35
8 12 9 55
7 13 0 42
8 13 0 48
8 13 1 48
8 13 2 48
8 13 3 48
9 13 6 54
8 13 8 48
6 13 9 36
8 14 2 39
4 14 3 19
8 14 5 39
8 15 5 32
8 15 7 32
10 15 9 36
1 16 1 3
3 16 2 9
8 16 2 23
9 16 4 27
8 16 5 23
8 16 6 23
8 16 8 23
7 17 0 14
8 17 0 16
5 17 1 10
8 17 4 16
7 17 5 14
8 17 5 16
9 17 5 18
8 17 6 16
8 17 7 16
9 17 7 18
8 17 8 16
9 18 0 9
8 18 3 7
6 18 4 5
3 18 7 3
4 18 7 3
8 18 7 7
4 18 8 3
9 18 9 9
11 5 3 48
11 5 4 48
11 14 3 40
11 14 4 40
11 18 4 8
2 18 5 1
11 18 8 8
12 8 0 62
12 8 3 62
12 9 3 70
12 3 4 28
12 7 4 56
12 8 4 62
12 4 8 34
12 8 8 62
12 2 9 20
12 5 9 42
12 7 9 56
12 11 9 56
12 12 4 48
12 13 8 42
12 14 9 34
12 16 4 20
12 16 9 20
12 17 0 14
12 17 3 14
12 17 4 14
12 17 8 14
13 6 0 42
13 2 4 18
13 4 4 30
13 7 9 48
13 11 4 48
13 13 4 36
13 15 0 24
13 16 9 18
14 9 4 50
14 6 5 34
14 7 5 40
14 15 5 20
14 16 5 14
14 18 2 4
15 5 1 24
15 6 1 28
15 8 2 36
15 8 4 36
15 5 6 24
15 8 6 36
15 14 1 20
15 14 6 20
15 15 1 16
15 17 2 8
15 17 4 8
15 17 6 8
15 18 2 4
15 18 4 4
15 18 6 4
16 6 0 20
16 5 3 18
16 7 3 24
16 8 4 26
16 5 5 18
16 6 6 20
16 6 8 20
16 4 9 14
16 13 9 18
16 14 3 14
16 14 5 14
16 15 0 12
16 15 6 12
16 15 8 12
16 16 3 8
16 17 4 6
16 18 1 2
17 4 0 10
17 5 0 12
17 6 0 14
17 2 1 6
17 4 1 10
17 5 1 12
17 6 1 14
17 9 1 20
17 3 2 8
17 6 2 14
17 7 2 16
17 8 2 18
17 9 2 20
17 4 3 10
17 6 3 14
17 3 4 8
17 8 4 18
17 2 5 6
17 3 5 8
17 6 5 14
17 8 5 18
17 3 6 8
17 4 6 10
17 6 6 14
17 8 6 18
17 4 7 10
17 6 7 14
17 7 7 16
17 4 8 10
17 5 9 12
17 11 1 16
17 11 5 16
17 12 2 14
17 12 4 14
17 12 5 14
17 12 6 14
17 13 0 12
17 13 1 12
17 13 3 12
17 13 6 12
17 13 7 12
17 13 8 12
17 14 0 10
17 14 1 10
17 14 9 10
17 15 0 8
17 15 1 8
17 15 2 8
17 15 3 8
17 15 5 8
17 15 6 8
17 15 7 8
17 16 2 6
17 16 7 6
17 17 2 4
17 17 4 4
17 17 5 4
17 17 6 4
17 18 0 2
17 18 3 2
17 18 5 2
17 18 6 2
17 18 8 2
18 7 0 8
18 4 2 4
18 7 2 8
18 1 3 2
18 7 3 8
18 5 4 6
18 8 4 8
18 9 4 10
18 7 5 8
18 8 5 8
18 1 7 2
18 7 9 8
18 10 3 8
18 10 7 8
18 13 2 6
18 14 4 4
18 16 0 2
18 16 2 2
18 16 3 2
18 16 5 2
18 16 9 2
18 17 4 2
18 17 5 2
A list of all 2-digit and 3-digit numbers that require more than 10
additions to produce palindromes with their palindromes.
Num. Additions Palindrome
89 24 8813200023188
98 24 8813200023188
167 11 88555588
177 15 8836886388
187 23 8813200023188
266 11 88555588
276 15 8836886388
286 23 8813200023188
365 11 88555588
375 15 8836886388
385 23 8813200023188
563 11 88555588
573 15 8836886388
583 23 8813200023188
662 11 88555588
672 15 8836886388
682 23 8813200023188
739 17 5233333325
761 11 88555588
771 15 8836886388
781 23 8813200023188
829 10 88555588
849 14 8836886388
860 11 88555588
869 22 8813200023188
870 15 8836886388
880 23 8813200023188
899 17 133697796331
928 10 88555588
937 17 5233333325
948 14 8836886388
968 22 8813200023188
998 17 133697796331
Maximum number of additions rquired when palindrome is found:
24 for 2-digit numbers.
23 for 3-digit numbers.
21 for 4-digit numbers.
55 for 5-digit numbers.
Attempt at a palindrome production with the number 196 by the special scheme of
repeated additions with the same digits in reverse order (carried to 75 digits).
Additions Results
0 196
1 887
2 1675
3 7436
4 13783
5 52514
6 94039
7 187088
8 1067869
9 10755470
10 18211171
11 35322452
12 60744805
13 111589511
14 227574622
15 454050344
16 897100798
17 1794102596
18 8746117567
19 16403234045
20 70446464506
21 130992928913
22 450822227944
23 900544455998
24 1800098901007
25 8801197801088
26 17602285712176
27 84724043932847
28 159547977975595
29 755127757721546
30 1400255515443103
31 4413700670963144
32 8827391431036288
33 17653692772973576
34 85191620502609247
35 159482241005228405
36 664304741147513356
37 1317620482294916822
38 3603815405135183953
39 7197630720180367016
40 13305261530450734933
41 47248966933966985264
42 93507933867933969538
43 177104867844767940077
44 947154635293536341848
45 1795298270686072793597
46 9749270977546801719568
47 18408442064004592449047
48 92502871604050616929528
49 175095833209091234750057
50 925153265399993573340628
51 1751196640799987135692157
52 9264161958699957602603728
53 17537224026299926194218357
54 92918473189299188236491928
55 175837936477498486373973857
56 934217310162393261013712428
57 1758434620324786522027424867
58 9442681822581660752291773438
59 17786453745152322604573635887
60 96640091285774647759309104658
61 182280281681549295517528109327
62 906182107397142240703710191608
63 1712373124704184482497411473217
64 8836114272647029296571625205388
65 17671139534403958504034349321776
66 85383533877444544434477942439447
67 159876958854887988978955775977805
68 668656536414767878767414635656756
69 1326313072829535757534829271313622
70 3589444802113893332894111974449853
71 7178889593228875666877224058899706
72 13258878097456662332665448018788423
73 45747659181913285659330927106673654
74 91385319354816681317562845302348408
75 171869639709643252636224690693706727
76 899477035806065888888571598630674898
77 1797953072701241777777132207161449896
78 8787394689723559555548553279865047867
79 16474800379447118011108106559729985745
80 71233793175007298122189281057030833206
81 131467596250025596244378551114170566423
82 456132667661181469687074071166866330554
83 911166336322351940474038252333632562208
84 1713431572655604770948087405557266223327
85 8946658200210652579438861471120017566498
86 17893315300422394267788614031240046132996
87 87816479304635435956564863353640397472867
88 164643958609270772803130816807280794934745
89 712083455691979390834439093880187654281206
90 1314265912473067781768877187859384208661423
91 4555933937312655599557549065463126404285554
92 9111757983526301209015109021025263797681108
93 17123625957151502418030218042061517695252227
94 89348885628667526499233299462576693647884398
95 178697760268335052998466598925153376306768796
96 876565363941686582894131498175687238374565667
97 1643130837774473154788262996461373387738131345
98 7074449215608204801780891870975118165118444806
99 13158897331226320592562872742059146230247889513
100 44757771534490515617290699271561508443627774644
101 89405544168971032134590308543213017887145550388
102 177711098347842063369170618086336035873290100886
103 865712190726372697049986690049696284617180218657
104 1622524272442855393990083379990492558244271436225
105 6848865996871408334989817180984428140686995688486
106 13697731993731826579880634370878766182473991376972
107 41665051931159993367687977979776328996213905156603
108 72330202862429975735485955958452668991327820213217
109 143561405734749962360971911916906426983754640416544
110 589175452192139586970591031095969696931192144581885
111 1177360893483279283940181161291049382862483399153870
112 1960880827325962123342102773101543212586327379791581
113 3812860564562814246793116545113976425281564660672272
114 6535621229214639493586232001227952849464219311354455
115 12080152368339288976183453003554806798828348532619811
116 23971775952722178737028983038992974787121734857727832
117 47844551796434357484958966077975048574244460815445764
118 94599003602878605069016943144960997049587930530990638
119 178208907106857199148923887279922093100275751161090187
120 959299068264429200539153860068251935092034352870893058
121 1809697146517859491078306720136603870094958815731886017
122 8916578521706454391861373030412642572044545972149855098
123 17822167934501908794613835170716374253979092043408611296
124 87033848368531006729861196877870205903760002587384734167
125 163177596747051013460811404755739322796520016173769567245
126 705943564118661039158035342313143440860830166921465338606
127 1312777128248322077226079683626386971712760333732930688113
128 4431637520621652749397876519890256677940462572161148460244
129 8852285932234405389895643040879413465879935133421405821588
130 17703570973477720789681286190659816931869770177743801644176
131 84848181808254828586495248086268985150568472955181709174947
132 159795372526410756073000407072537069410037055800462527359795
133 757749097790419306803015367807807773410407712815087800957746
134 1405508106570937524507029745516516536920716316729185591905503
135 4460600062390213660677326101672672016127770574119941609960544
136 8911299123889328411454542204435433032365531237240874210021188
137 17722499248669755732810174507780777054820072385480757429942386
138 86047491724378214059813019585489547601921896141277441729365157
139 161203884438855428229625930260088006192953791182564784448839225
140 684142728926320709426985221860968068232480714007123618937141386
141 1367284468742642409844069454721837136355070338914147248764382872
142 4150119147170056608174774991039218410904674827956609727409210503
143 7200248194449123205459539081187347712899449546023110444828321017
144 14301486478889236411918989063364785524708809091046329889746741044
145 58316251277781600431009869805923531860807791002509628777215151385
146 116631402555564290951029640612737064811704681015910247554430412770
147 193845437011306310461216047731197802027751601175002713109634549381
148 377790873912623511032322205451406593165492213339016316220369097772
149 655581836935237121965634500012802197319994436569131642439747195545
150 1201173584869483253931268999926593405529999873138253374979385381101
151 2213009424664216782245058999181637361829998494531777224664239092122
152 4425918749328444553600007998463274723649996999954653349328488095244
153 8851827597567878118200004997926549447298994000018207797567966290488
154 17692754295225855146300009996853998903596988000046326585225923572076
155 84720287247484417510300098966384988839466978000410482437485169301747
156 159430683405957845911700186932878877787833967000712053885959447504495
157 753836428365546196128700956271666656666073648007831602645463833539446
158 1398771766730092402267401802642333313332246307015653294291027658177803
159 4486490333932017325832508839064666446664708388063275337191404329956734
160 8863089567973934661556117677139332893329317776115660574293797660903578
161 17616180235947859412221234454278566875668635543232212238687595320707266
162 83886882595526542633444469007965224742255880986444433734562548528868937
163 157873765180053086366888937916820449484512851082888867359125108057737775
164 735611515981575040135777218075035934428541470822777531039475189625116526
165 1361223042963149970271554446149181758868072041635555062080050379140233063
166 4964543462693650772877109807551890447439891458080106782879464071543454694
167 9929086914398300555753120616093879794880873015169124565650028034186909388
168 18768183728706501121407340231197660679860656921329338141200066968383718687
169 97449922115672501335590732544163267577467336034533708553310627751121905468