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June 20th, 2005
05:48 pm - Athena, you're wrong.
First, the original text:
(15:19:25) Athena: Do you know what is special about 196?
(15:19:45) CERisE8192: It's 14^2
(15:19:56) Athena: well, there's that
(15:20:37) Athena: But also, it's not a palindromic number, and never becomes one no matter how many times you flip the digits and add it to itself
(15:20:49) Athena: Every positive integer that comes before it is
(15:20:56) Athena: In base 10 at least
(15:21:02) Athena: brb
(15:23:43) CERisE8192: Hmm. I'm not certain if I believe that. What differentiates it from 169 (13^2)?
(15:32:21) Athena: 169 + 961 = 1130
(15:32:45) Athena: 1130 + 0311 = 1441
(15:32:49) Athena: see?
(15:32:58) CERisE8192: Oh! That sort of flipping digits.
(15:33:04) CERisE8192: Hmm. I'm not sure if I believe that.
(15:33:14) Athena: just try
(15:33:22) Athena: 196 never becomes palindromic
(15:35:12) Athena: 196 + 691 = 887
(15:35:44) Athena: 887 + 788 = 1675
(15:36:13) CERisE8192: Tsk. This is precisely what computers are good at.
(15:36:22) Athena: yeah good point
Turn 1: 196 + 691 = 887
Turn 2: 887 + 788 = 1675
Turn 3: 1675 + 5761 = 7436
Turn 4: 7436 + 6347 = 13783
Turn 5: 13783 + 38731 = 52514
Turn 6: 52514 + 41525 = 94039
Turn 7: 94039 + 93049 = 187088
Turn 8: 187088 + 880781 = 1067869
Turn 9: 1067869 + 9687601 = 10755470
Turn 10: 10755470 + 7455701 = 18211171
Turn 11: 18211171 + 17111281 = 35322452
Turn 12: 35322452 + 25422353 = 60744805
Turn 13: 60744805 + 50844706 = 111589511
Turn 14: 111589511 + 115985111 = 227574622
Turn 15: 227574622 + 226475722 = 454050344
Turn 16: 454050344 + 443050454 = 897100798
Turn 17: 897100798 + 897001798 = 1794102596
Turn 18: 1794102596 + 6952014971 = 8746117567
Turn 19: 8746117567 + 7657116478 = 16403234045
Turn 20: 16403234045 + 54043230461 = 70446464506
Turn 21: 70446464506 + 60546464407 = 130992928913
Turn 22: 130992928913 + 319829299031 = 450822227944
Turn 23: 450822227944 + 449722228054 = 900544455998
Turn 24: 900544455998 + 899554445009 = 1800098901007
Turn 25: 1800098901007 + 7001098900081 = 8801197801088
Turn 26: 8801197801088 + 8801087911088 = 17602285712176
Turn 27: 17602285712176 + 67121758220671 = 84724043932847
Turn 28: 84724043932847 + 74823934042748 = 159547977975595
Turn 29: 159547977975595 + 595579779745951 = 755127757721546
Turn 30: 755127757721546 + 645127757721557 = 1400255515443103
Turn 31: 1400255515443103 + 3013445155520041 = 4413700670963144
Turn 32: 4413700670963144 + 4413690760073144 = 8827391431036288
Turn 33: 8827391431036288 + 8826301341937288 = 17653692772973576
Turn 34: 17653692772973576 + 67537927729635671 = 85191620502609247
Turn 35: 85191620502609247 + 74290620502619158 = 159482241005228405
Turn 36: 159482241005228405 + 504822500142284951 = 664304741147513356
Turn 37: 664304741147513356 + 653315741147403466 = 1317620482294916822
Turn 38: 1317620482294916822 + 2286194922840267131 = 3603815405135183953
Turn 39: 3603815405135183953 + 3593815315045183063 = 7197630720180367016
Turn 40: 7197630720180367016 + 6107630810270367917 = 13305261530450734933
Turn 41: 13305261530450734933 + 15496961329806698715 = 10355478786547882032
Turn 42: 10355478786547882032 + 4582130495077903685 = 14937609281625785717
Turn 43: 14937609281625785717 + 16418520397162019093 = 12909385605078253194
Turn 44: 12909385605078253194 + 12241798903239287689 = 6704440434607989267
Turn 45: 6704440434607989267 + 7629897064340444076 = 14334337498948433343
Turn 46: 14334337498948433343 + 15886740915763791725 = 11774334341002673452
Turn 47: 11774334341002673452 + 6990875940633796095 = 318466207926917931
Turn 48: 318466207926917931 + 139719629702664813 = 458185837629582744
Turn 49: 458185837629582744 + 447285926738581854 = 905471764368164598
Turn 50: 905471764368164598 + 895461863467174509 = 1800933627835339107
Turn 51: 1800933627835339107 + 7019335387263390081 = 8820269015098729188
Turn 52: 8820269015098729188 + 8819278905109620288 = 17639547920208349476
Turn 53: 17639547920208349476 + 12154147981845938823 = 11346951828344736683
Turn 54: 11346951828344736683 + 1770256235396861079 = 13117208063741597762
Turn 55: 13117208063741597762 + 8332770662370719515 = 3003234652402765661
Turn 56: 3003234652402765661 + 1665672042564323003 = 4668906694967088664
Turn 57: 4668906694967088664 + 4668807694966098664 = 9337714389933187328
Turn 58: 9337714389933187328 + 8237813399834177339 = 17575527789767364667
Turn 59: 17575527789767364667 + 2859400503934351107 = 1988184219992164158
Turn 60: 1988184219992164158 + 8514612999124818891 = 10502797219116983049
Turn 61: 10502797219116983049 + 1805240822731962421 = 12308038041848945470
Turn 62: 12308038041848945470 + 7454984814083080321 = 1316278782222474175
Turn 63: 1316278782222474175 + 5714742222878726131 = 7031021005101200306
Turn 64: 7031021005101200306 + 6030021015001201307 = 13061042020102401613
Turn 65: 13061042020102401613 + 13163676028314464415 = 7777973974707314412
Turn 66: 7777973974707314412 + 2144137074793797777 = 9922111049501112189
Turn 67: 9922111049501112189 + 9812111059401112299 = 1287478035192672872
Turn 68: 1287478035192672872 + 2782762915308747821 = 4070240950501420693
Turn 69: 4070240950501420693 + 3960241050590420704 = 8030482001091841397
Turn 70: 8030482001091841397 + 7931481901002840308 = 15961963902094681705
Turn 71: 15961963902094681705 + 13825160873517813719 = 11340380701902943808
Turn 72: 11340380701902943808 + 7047944615870097847 = 18388325317773041655
Turn 73: 18388325317773041655 + 273805550223733533 = 215386794287223572
Turn 74: 215386794287223572 + 275322782497683512 = 490709576784907084
Turn 75: 490709576784907084 + 480709487675907094 = 971419064460814178
Turn 76: 971419064460814178 + 871418064460914179 = 1842837128921728357
Turn 77: 1842837128921728357 + 7538271298217382481 = 9381108427139110838
Turn 78: 9381108427139110838 + 8380119317248011839 = 17761227744387122677
Turn 79: 17761227744387122677 + 3835202049934010307 = 3149685720611581368
Turn 80: 3149685720611581368 + 8631851160275869413 = 11781536880887450781
Turn 81: 11781536880887450781 + 258734735153967095 = 12040271616041417876
Turn 82: 12040271616041417876 + 12531181840488549173 = 6124709382820415433
Turn 83: 6124709382820415433 + 3345140282839074216 = 9469849665659489649
Turn 84: 9469849665659489649 + 9469849565669489649 = 492955157619427682
Turn 85: 492955157619427682 + 286724916751559294 = 779680074370986976
Turn 86: 779680074370986976 + 679689073470086977 = 1459369147841073953
Turn 87: 1459369147841073953 + 3593701487419639541 = 5053070635260713494
Turn 88: 5053070635260713494 + 4943170625360703505 = 9996241260621416999
Turn 89: 9996241260621416999 + 9996141260621426999 = 1545638447533292382
Turn 90: 1545638447533292382 + 2832923357448365451 = 4378561804981657833
Turn 91: 4378561804981657833 + 3387561894081658734 = 7766123699063316567
Turn 92: 7766123699063316567 + 7656133609963216677 = 15422257309026533244
Turn 93: 15422257309026533244 + 7340073942956119219 = 4315587178273100847
Turn 94: 4315587178273100847 + 7480013728717855134 = 11795600906990955981
Turn 95: 11795600906990955981 + 509165887191108095 = 12304766794182064076
Turn 96: 12304766794182064076 + 11705795928638085473 = 5563818649110597933
Turn 97: 5563818649110597933 + 3397950119468183655 = 8961768768578781588
Turn 98: 8961768768578781588 + 8851878758678671698 = 17813647527257453286
Turn 99: 17813647527257453286 + 12895243051445977023 = 12262146504993878693
Turn 100: 12262146504993878693 + 2794351793145022989 = 15056498298138901682
Turn 101: 15056498298138901682 + 10164239115579913435 = 6773993340009263501
Turn 102: 6773993340009263501 + 1053629000433993776 = 7827622340443257277
Turn 103: 7827622340443257277 + 7727523440432267287 = 15555145780875524564
Turn 104: 15555145780875524564 + 9649069661335052319 = 6757471368501025267
Turn 105: 6757471368501025267 + 7625201058631747576 = 14382672427132772843
Turn 106: 14382672427132772843 + 16380979098718076725 = 12316907452141297952
Turn 107: 12316907452141297952 + 7532470051761409705 = 1402633430193156041
Turn 108: 1402633430193156041 + 1406513910343362041 = 2809147340536518082
Turn 109: 2809147340536518082 + 2808156350437419082 = 5617303690973937164
Turn 110: 5617303690973937164 + 4617393790963037165 = 10234697481936974329
Turn 111: 10234697481936974329 + 114243549931885121 = 10348941031868859450
Turn 112: 10348941031868859450 + 5495886813014984301 = 15844827844883843751
Turn 113: 15844827844883843751 + 15734838844872844851 = 13132922616047136986
Turn 114: 13132922616047136986 + 13622941840494268283 = 8309120382831853653
Turn 115: 8309120382831853653 + 3563581382830219038 = 11872701765662072691
Turn 116: 11872701765662072691 + 1180282583001176195 = 13052984348663248886
Turn 117: 13052984348663248886 + 13544004463220270183 = 8150244738173967453
Turn 118: 8150244738173967453 + 3547693718374420518 = 11697938456548387971
Turn 119: 11697938456548387971 + 17978384565483979611 = 11229578948322815966
Turn 120: 11229578948322815966 + 11611590163858937363 = 4394425038472201713
Turn 121: 4394425038472201713 + 3171022748305244934 = 7565447786777446647
Turn 122: 7565447786777446647 + 7466447776877445657 = 15031895563654892304
Turn 123: 15031895563654892304 + 3436357489140709819 = 21508979086050507
Turn 124: 21508979086050507 + 70505068097980512 = 92014047184031019
Turn 125: 92014047184031019 + 91013048174041029 = 183027095358072048
Turn 126: 183027095358072048 + 840270853590720381 = 1023297948948792429
Turn 127: 1023297948948792429 + 9242978498497923201 = 10266276447446715630
Turn 128: 10266276447446715630 + 3651764474467266201 = 13918040921913981831
Turn 129: 13918040921913981831 + 13818931912904081931 = 9290228761108512146
Turn 130: 9290228761108512146 + 6412158011678220929 = 15702386772786733075
Turn 131: 15702386772786733075 + 1693536506639665903 = 17395923279426398978
Turn 132: 17395923279426398978 + 14202386202394752907 = 13151565408111600269
Turn 133: 13151565408111600269 + 3966890811908757051 = 17118456220020357320
Turn 134: 17118456220020357320 + 2375302002265481171 = 1047014148576286875
Turn 135: 1047014148576286875 + 5786826758414107401 = 6833840906990394276
Turn 136: 6833840906990394276 + 6724930996090483386 = 13558771903080877662
Turn 137: 13558771903080877662 + 8231063957208233915 = 3343091786579559961
Turn 138: 3343091786579559961 + 1699559756871903433 = 5042651543451463394
Turn 139: 5042651543451463394 + 4933641543451562405 = 9976293086903025799
Turn 140: 9976293086903025799 + 9975203096803926799 = 1504752109997400982
Turn 141: 1504752109997400982 + 2890047999012574051 = 4394800109009975033
Turn 142: 4394800109009975033 + 3305799009010084934 = 7700599118020059967
Turn 143: 7700599118020059967 + 7699500208119950077 = 15400099326140010044
Turn 144: 15400099326140010044 + 7107516014979897219 = 4060871267410355647
Turn 145: 4060871267410355647 + 7465530147621780604 = 11526401415032136251
Turn 146: 11526401415032136251 + 15263123051410462511 = 8342780392733047146
Turn 147: 8342780392733047146 + 6417403372930872438 = 14760183765663919584
Turn 148: 14760183765663919584 + 11698448509319003509 = 8011888201273371477
Turn 149: 8011888201273371477 + 7741733721028881108 = 15753621922302252585
Turn 150: 15753621922302252585 + 3184988101783980903 = 491865950376681872
Turn 151: 491865950376681872 + 278186673059568194 = 770052623436250066
Turn 152: 770052623436250066 + 660052634326250077 = 1430105257762500143
Turn 153: 1430105257762500143 + 3410052677525010341 = 4840157935287510484
Turn 154: 4840157935287510484 + 4840157825397510484 = 9680315760685020968
Turn 155: 9680315760685020968 + 8690205860675130869 = 18370521621360151837
Turn 156: 18370521621360151837 + 28130017774300917 = 18398651639134452754
Turn 157: 18398651639134452754 + 8831955046196586149 = 8783862611621487287
Turn 158: 8783862611621487287 + 7827841261162683878 = 16611703872784171165
Turn 159: 16611703872784171165 + 776916506702056813 = 17388620379486227978
Turn 160: 17388620379486227978 + 14185292202464481907 = 13127168508241158269
Turn 161: 13127168508241158269 + 4051393912038414051 = 17178562420279572320
Turn 162: 17178562420279572320 + 2327597202426587171 = 1059415548996607875
Turn 163: 1059415548996607875 + 5787066998455149501 = 6846482547451757376
Turn 164: 6846482547451757376 + 6737571547452846486 = 13584054094904603862
Turn 165: 13584054094904603862 + 8383896875335496915 = 3521206896530549161
Turn 166: 3521206896530549161 + 1619450356986021253 = 5140657253516570414
Turn 167: 5140657253516570414 + 4140756153527560415 = 9281413407044130829
Turn 168: 9281413407044130829 + 9280314407043141829 = 114983740377721042
Turn 169: 114983740377721042 + 240127773047389411 = 355111513425110453
Turn 170: 355111513425110453 + 354011524315111553 = 709123037740222006
Turn 171: 709123037740222006 + 600222047730321907 = 1309345085470543913
Turn 172: 1309345085470543913 + 3193450745805439031 = 4502795831275982944
Turn 173: 4502795831275982944 + 4492895721385972054 = 8995691552661954998
Turn 174: 8995691552661954998 + 8994591662551965998 = 17990283215213920996
Turn 175: 17990283215213920996 + 14562699030109555123 = 14106238171613924503
Turn 176: 14106238171613924503 + 12096187543473708525 = 7755681641378081412
Turn 177: 7755681641378081412 + 2141808731461865577 = 9897490372839946989
Turn 178: 9897490372839946989 + 9896499382730947989 = 1347245681861343362
Turn 179: 1347245681861343362 + 2633431681865427431 = 3980677363726770793
Turn 180: 3980677363726770793 + 3970776273637760893 = 7951453637364531686
Turn 181: 7951453637364531686 + 6861354637363541597 = 14812808274728073283
Turn 182: 14812808274728073283 + 1343594599861718609 = 16156402874589791892
Turn 183: 16156402874589791892 + 11373054474110913545 = 9082713274991153821
Turn 184: 9082713274991153821 + 1283511994723172809 = 10366225269714326630
Turn 185: 10366225269714326630 + 3662341796252266301 = 14028567065966592931
Turn 186: 14028567065966592931 + 13929566956076582041 = 9511389948333623356
Turn 187: 9511389948333623356 + 6533263338499831159 = 16044653286833454515
Turn 188: 16044653286833454515 + 14651945720816540829 = 12249854933940443728
Turn 189: 12249854933940443728 + 8947428639107687757 = 2750539499338579869
Turn 190: 2750539499338579869 + 9689758339949350572 = 12440297839287930441
Turn 191: 12440297839287930441 + 14403978293879204421 = 8397532059457583246
Turn 192: 8397532059457583246 + 6423857549502357938 = 14821389608959941184
Turn 193: 14821389608959941184 + 11221507833279209609 = 7596153368529599177
Turn 194: 7596153368529599177 + 7719959258633516957 = 15316112627163116134
Turn 195: 15316112627163116134 + 6267648025202058119 = 3137016578655622637
Turn 196: 3137016578655622637 + 7362265568756107313 = 10499282147411729950
Turn 197: 10499282147411729950 + 5992711474128299401 = 16491993621540029351
Turn 198: 16491993621540029351 + 15392004512639919461 = 13437254060470397196
Turn 199: 13437254060470397196 + 13839075184916618583 = 8829585171677464163
Turn 200: 8829585171677464163 + 3614647761715859288 = 12444232933393323451
Turn 201: 12444232933393323451 + 15432339333923244421 = 9429828193607016256
Turn 202: 9429828193607016256 + 6526107063918289249 = 15955935257525305505
Turn 203: 15955935257525305505 + 13656864427834852719 = 11166055611650606608
Turn 204: 11166055611650606608 + 6873629316816859647 = 18039684928467466255
Turn 205: 18039684928467466255 + 18372988335529589849 = 17965929190287504488
Turn 206: 17965929190287504488 + 14653601914354750507 = 14172787030932703379
Turn 207: 14172787030932703379 + 5097003534530969061 = 823046491754120824
Turn 208: 823046491754120824 + 428021457194640328 = 1251067948948761152
Turn 209: 1251067948948761152 + 2511678498497601521 = 3762746447446362673
Turn 210: 3762746447446362673 + 3762636447446472673 = 7525382894892835346
Turn 211: 7525382894892835346 + 6435382984982835257 = 13960765879875670603
Turn 212: 13960765879875670603 + 12160913824147155315 = 7674935630313274302
Turn 213: 7674935630313274302 + 2034723130365394767 = 9709658760678669069
Turn 214: 9709658760678669069 + 9609668760678569079 = 872583447647686532
Turn 215: 872583447647686532 + 235686746744385278 = 1108270194392071810
Turn 216: 1108270194392071810 + 181702934910728011 = 1289973129302799821
Turn 217: 1289973129302799821 + 1289972039213799821 = 2579945168516599642
Turn 218: 2579945168516599642 + 2469956158615499752 = 5049901327132099394
Turn 219: 5049901327132099394 + 4939902317231099405 = 9989803644363198799
Turn 220: 9989803644363198799 + 9978913634463089899 = 1521973205116737082
Turn 221: 1521973205116737082 + 2807376115023791251 = 4329349320140528333
Turn 222: 4329349320140528333 + 3338250410239439234 = 7667599730379967567
Turn 223: 7667599730379967567 + 7657699730379957667 = 15325299460759925234
Turn 224: 15325299460759925234 + 6359507559080149119 = 3238062946130522737
Turn 225: 3238062946130522737 + 7372250316492608323 = 10610313262623131060
Turn 226: 10610313262623131060 + 6013132626231301601 = 16623445888854432661
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What is it with those tags and my friends list. =( I'm not sure. Just for fun, I checked /users/theswede/friends and didn't see anything particularly wrong. But then again, I didn't see any tags at all. Did something particularly evil occur? The chat transcript doesn't wrap, making the page wider than the window. Not sure why. That can't be right. The number has been tested to a sum with a million digits and it never becomes a palindrome; at least that's what I read (and it's quite possible whoever wrote that was BSing it completely). Also, there just seems to be something really off about this proof, namely that the dramatic slope of the right margin tapers off at around Turn 41. I don't really have any means to go through this summing game efficiently, but I'm guessing that can't be right. The numbers should be increasing more rapidly than that. Well, in any case, this is where I read that 196 is not palindromic: http://www.everything2.com/index.pl?node_id=1238477Look at the numbers in line 42! Exactly right. At line 41 it overflows. Tsk, I should've checked for it.
Anyway, point conceded. I'll need to switch the way I compute it. I'm looking at this a bit harder, it seems like this is dependent on which base it uses. For example, consider that the inverse of 196 in binary is 67, rather than 691.
The next logical question is whether there's a correlation between the base and numbers that cycle in this way.
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