Les 20120 nombres SL

(calculés par David Wilson).

Les chiffres qui entrent dans l’écriture d’un nombre SL (SL pour Skolem-Langford) vont toujours par paires, et chaque paire de chiffres est unique. De plus, entre deux chiffres k il y a exactement k chiffres.

Prenons le 8^e SL de la liste ci-dessous par exemple, 14130043 -- il y a bien 0 chiffre entre les deux « 0 », 1 chiffre entre les deux « 1 », 3 chiffres entre les deux « 3 » et 4 chiffres entre les deux « 4 ». Le dernier SL est 978416154798652002.

Les SL-forts obéissent à la même règle mais toutes les paires [0,1,2,... k] sont présentes. Les SL-faibles sont évidemment les SL qui ne sont pas forts (2002, par exemple, où k=1 n’est pas illustré). Les premiers SL-forts sont donc 12132003, 1214230043, 1312432004, 2342131400... et le dernier est 867315136875420024.

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1=2002, 2=131003, 3=231213, 4=300131, 5=312132, 6=420024, 7=12132003, 8=14130043, 9=15120025, 10=23121300, 11=23421314, 12=25121005, 13=25320035, 14=30023121, 15=31213200, 16=31413004, 17=34003141, 18=40031413, 19=41312432, 20=45001415, 21=45121425, 22=45300435, 23=50012152, 24=51410054, 25=52002151, 26=52412154, 27=53002352, 28=53400354, 29=61310036, 30=62312136, 31=63001316, 32=63121326, 33=64200246, 34=1214230043, 35=1312432004, 36=1514002542, 37=1613002362, 38=1613400364, 39=1615200265, 40=1714200247, 41=2342131400, 42=2352430054, 43=2362131006, 44=2412134003, 45=2452004151, 46=2462314136, 47=2562001516, 48=2562300536, 49=2612130063, 50=2632003161, 51=2632413164, 52=2642131463, 53=2742001417, 54=2742300437, 55=3004312142, 56=3161320026, 57=3400324121, 58=3425324005, 59=3461314006, 60=3564300546, 61=3600312162, 62=3625320065, 63=3641312462, 64=3645300465, 65=3724320047, 66=3751310057, 67=3752312157, 68=4002342131, 69=4005241215, 70=4131243200, 71=4161340036, 72=4235243005, 73=4263241316, 74=4500342532, 75=4512142500, 76=4560041516, 77=4562342536, 78=4613142362, 79=4615140065, 80=4630043161, 81=4635243265, 82=4700241217, 83=4712142007, 84=4753141357, 85=5003425324, 86=5004235243, 87=5121425004, 88=5241215400, 89=5261215006, 90=5264215146, 91=5364235246, 92=5600235263, 93=5600415164, 94=5620025161, 95=5623425364, 96=5640035463, 97=5700315137, 98=5713125327, 99=5740025427, 100=5741315437, 101=6001312632, 102=6004131643, 103=6005121625, 104=6131423624, 105=6151002652, 106=6151400654, 107=6200231613, 108=6231213600, 109=6300431614, 110=6312132600, 111=6314132642, 112=6350032652, 113=6352432654, 114=6415124625, 115=6425324635, 116=6450034653, 117=6700121627, 118=6714100647, 119=6720021617, 120=6724121647, 121=6730023627, 122=6734003647, 123=6752002657, 124=7002412174, 125=7121420074, 126=7141002472, 127=7161200276, 128=7235213175, 129=7245200475, 130=7261210076, 131=7263200376, 132=7315130075, 133=7340032472, 134=7345131475, 135=7400234273, 136=7420024171, 137=7460014176, 138=7461214276, 139=7463004376, 140=7500131573, 141=7512132573, 142=7531413574, 143=7562002576, 144=8002312138, 145=8003121328, 146=8121320038, 147=8141300438, 148=8151200258, 149=8231213008, 150=8234213148, 151=8251210058, 152=8253200358, 153=8300231218, 154=8312132008, 155=8314130048, 156=8340031418, 157=8400314138, 158=8413124328, 159=8450014158, 160=8451214258, 161=8453004358, 162=8500121528, 163=8514100548, 164=8520021518, 165=8524121548, 166=8530023528, 167=8534003548, 168=8613100368, 169=8623121368, 170=8630013168, 171=8631213268, 172=8642002468, 173=121623400364, 174=131623420064, 175=131643002462, 176=131753200257, 177=141362432006, 178=141625420065, 179=141753400357, 180=151264250046, 181=151640052462, 182=151734253247, 183=151742352437, 184=161003426324, 185=161004236243, 186=161500426524, 187=161740026427, 188=161753006357, 189=171264200746, 190=171350032752, 191=171352432754, 192=171425324735, 193=171450034753, 194=171460024726, 195=171635003765, 196=181245200485, 197=181263200386, 198=181340032482, 199=181400234283, 200=181463004386, 201=181562002586, 202=181742002487, 203=191253200359, 204=191453004359, 205=191530023529, 206=191534003549, 207=191642002469, 208=234263141006, 209=236253400654, 210=238243001418, 211=245261415006, 212=246200431613, 213=246231413600, 214=247235413175, 215=247261410076, 216=247263400376, 217=248231413008, 218=248251410058, 219=248253400358, 220=253264350046, 221=256200451614, 222=257230053171, 223=257263151376, 224=258214150048, 225=258240051418, 226=263241316400, 227=264200346131, 228=264213146300, 229=264215146005, 230=264250046151, 231=267200416174, 232=267240036473, 233=267245006475, 234=268200316138, 235=268241316438, 236=268250016158, 237=268253006358, 238=271215300735, 239=273264300746, 240=274260041716, 241=275214135743, 242=275261315736, 243=275264005746, 244=278214100748, 245=278234003748, 246=281213400384, 247=283245300485, 248=283261310086, 249=284215140085, 250=284230043181, 251=284263141386, 252=285200415184, 253=285240035483, 254=285260015186, 255=285263005386, 256=286200131683, 257=286215100685, 258=286231413684, 259=286235003685, 260=293251310059, 261=294253141359, 262=295200315139, 263=295241315439, 264=296214100649, 265=296234003649, 266=297213100379, 267=297230013179, 268=300632412164, 269=316134002642, 270=317135200275, 271=318134200248, 272=342632400161, 273=345731415007, 274=347531412572, 275=348131420028, 276=348631410068, 277=348632412168, 278=352632450064, 279=352732151007, 280=356730051617, 281=356734151647, 282=357131450074, 283=357430054171, 284=358234250048, 285=364131246200, 286=364235246005, 287=367235216175, 288=367531416574, 289=368231216008, 290=368234216148, 291=368530026528, 292=368534006548, 293=370035121725, 294=372632400764, 295=374235241715, 296=374630042762, 297=374635141765, 298=375131425724, 299=375231215700, 300=375631415764, 301=378234200748, 302=378430024728, 303=378632002768, 304=380032412184, 305=382432004181, 306=382532400584, 307=384235240085, 308=384530042582, 309=385730015187, 310=385731215287, 311=386131002682, 312=386131400684, 313=386235200685, 314=386435004685, 315=386732002687, 316=392532001519, 317=394530041519, 318=395231215009, 319=395234215149, 320=395630015169, 321=395631215269, 322=396234200649, 323=396430024629, 324=397131200279, 325=397231210079, 326=397430014179, 327=397431214279, 328=397532002579, 329=400364231216, 330=400564121526, 331=413164320026, 332=416154002652, 333=417164200276, 334=418124320038, 335=418154200258, 336=423624300161, 337=425624005161, 338=425724315137, 339=426324131600, 340=426724001617, 341=426724300637, 342=427524131573, 343=428324131008, 344=428524001518, 345=428524300538, 346=450064251216, 347=451714350037, 348=456004352632, 349=456234253600, 350=457234253171, 351=457264250076, 352=458004251218, 353=458234253008, 354=458614150068, 355=458634253268, 356=460024326131, 357=460054236253, 358=461214236003, 359=461314236200, 360=463004326121, 361=463524326500, 362=463724326007, 363=463754316157, 364=467004236273, 365=467514136573, 366=468004316138, 367=468254216158, 368=468314136008, 369=468354236258, 370=468514126528, 371=468524326538, 372=470054131753, 373=470064121726, 374=471614002762, 375=475314135700, 376=475614135763, 377=478004121728, 378=478254200758, 379=478354131758, 380=478614100768, 381=478624121768, 382=478634003768, 383=481214230083, 384=481514002582, 385=481714200287, 386=483004312182, 387=483564300586, 388=483724320087, 389=485004235283, 390=485264215186, 391=485364235286, 392=486004131683, 393=486314132682, 394=486714100687, 395=486724121687, 396=486734003687, 397=491514300539, 398=491614200269, 399=493524321519, 400=493624320069, 401=495004315139, 402=495314135009, 403=496004121629, 404=496254200659, 405=496354131659, 406=497234213179, 407=497314130079, 408=497514100579, 409=497524121579, 410=497534003579, 411=500463524326, 412=500641512462, 413=500642532463, 414=500723521317, 415=500734513147, 416=514162542006, 417=517142532473, 418=517163500376, 419=518124520048, 420=524723541317, 421=526421514600, 422=526724500647, 423=527121530073, 424=528324530048, 425=528421514008, 426=528621510068, 427=528623500368, 428=531713520027, 429=536423524600, 430=536723521617, 431=537003512172, 432=537423524171, 433=537463514176, 434=538423524008, 435=538623520068, 436=538643500468, 437=560024526141, 438=561713526327, 439=562342536400, 440=567141536473, 441=567300536171, 442=568003526328, 443=568004516148, 444=568121526008, 445=568141526428, 446=571312532700, 447=571314532742, 448=571612532763, 449=572002531713, 450=572362531716, 451=574131543700, 452=574600542762, 453=578131523728, 454=578300531718, 455=578400524728, 456=578631513768, 457=580041512482, 458=580042532483, 459=580062512186, 460=581713500387, 461=582362530086, 462=582462514186, 463=582732513187, 464=582742500487, 465=584002542181, 466=584003542382, 467=584161540086, 468=586001512682, 469=586002532683, 470=586300532682, 471=586400534683, 472=586731513687, 473=590023521319, 474=590034513149, 475=591312532009, 476=591314530049, 477=591413524329, 478=591613500369, 479=592342531419, 480=592632513169, 481=592642500469, 482=594003541319, 483=594131543009, 484=596131523629, 485=596300531619, 486=596400524629, 487=597002512179, 488=597121520079, 489=597141500479, 490=597342532479, 491=597400514179, 492=597423524379, 493=600141362432, 494=600234263141, 495=600245261415, 496=600514162542, 497=600734263247, 498=600742362437, 499=600753161357, 500=612132463004, 501=612152460054, 502=613142362400, 503=617135263275, 504=617140062472, 505=618134263248, 506=618142362438, 507=620023461314, 508=623425364005, 509=623724360047, 510=625121465004, 511=627121460074, 512=627420064171, 513=628121360038, 514=628520061518, 515=628524161548, 516=631413264200, 517=635243265400, 518=635713165007, 519=637513162572, 520=638003261218, 521=638243261418, 522=638253260058, 523=638413164008, 524=638453264258, 525=640052462151, 526=640053462352, 527=641512462500, 528=641712462007, 529=642532463500, 530=642732463007, 531=642752460057, 532=647002462171, 533=647003462372, 534=647500462572, 535=648003461318, 536=648131463008, 537=648151460058, 538=648500461518, 539=670014162742, 540=670052462754, 541=671415364735, 542=672002461714, 543=672412164700, 544=673004362742, 545=673005361715, 546=673151362752, 547=678002362738, 548=678004161748, 549=678200261718, 550=678234263748, 551=678400364738, 552=678450064758, 553=680013162382, 554=680035263285, 555=680045161485, 556=681215260085, 557=681415264285, 558=681510062582, 559=681512462584, 560=682532463584, 561=682712160087, 562=682742161487, 563=683002362181, 564=683141362482, 565=683400364181, 566=683500362582, 567=683742362487, 568=685003465384, 569=685200265181, 570=685700265287, 571=685713165387, 572=685740065487, 573=690034263249, 574=690042362439, 575=690053161359, 576=691214260049, 577=691512362539, 578=692412164009, 579=693151360059, 580=693500361519, 581=695004265249, 582=695141365439, 583=697003161379, 584=697131263279, 585=697400264279, 586=697413164379, 587=697500161579, 588=697512162579, 589=697530063579, 590=700151237253, 591=700264217146, 592=700364237246, 593=700514137543, 594=700561317536, 595=700623427364, 596=713125327005, 597=713145327425, 598=716100427624, 599=716125327635, 600=716150037653, 601=718140027428, 602=718153007358, 603=720025317135, 604=723521317500, 605=723625317165, 606=724620047161, 607=728521317538, 608=728524007548, 609=728620017168, 610=728623007368, 611=730053417154, 612=731513427524, 613=734253247151, 614=734263247006, 615=734513147500, 616=736003427624, 617=738253217158, 618=738513127528, 619=738643007468, 620=740063427326, 621=741315437005, 622=742352437151, 623=742362437006, 624=746005427625, 625=746121427600, 626=746151437653, 627=748003427328, 628=748121427008, 629=748500427528, 630=748600417168, 631=748623427368, 632=750064257246, 633=751213257300, 634=751613457364, 635=752002357131, 636=753004357141, 637=753141357400, 638=753161357006, 639=753600357161, 640=758004257248, 641=758141357438, 642=758600257268, 643=758613157368, 644=758640057468, 645=780023427384, 646=780061217286, 647=781315237285, 648=781510037583, 649=782002417184, 650=782512137583, 651=782562007586, 652=783005317185, 653=783561317586, 654=784005247285, 655=784161247286, 656=784200247181, 657=784263247386, 658=784560047586, 659=786001417684, 660=786121427684, 661=786200237683, 662=786300437684, 663=786315137685, 664=790013127329, 665=790041317439, 666=790051217259, 667=791314237249, 668=791510027529, 669=791514007549, 670=791613007369, 671=792002317139, 672=792312137009, 673=792642007469, 674=793004317149, 675=793121327009, 676=793141327429, 677=793500327529, 678=793524327549, 679=793600317169, 680=793641317469, 681=794151247259, 682=794253247359, 683=794500347539, 684=794600247269, 685=794613147369, 686=796001317639, 687=796121327639, 688=796151007659, 689=796251217659, 690=796314137649, 691=796350037659, 692=800131423824, 693=800314132842, 694=800352432854, 695=800364131846, 696=800415124825, 697=800425324835, 698=800461314836, 699=800612132863, 700=800625121865, 701=800631413864, 702=800724121847, 703=812152400854, 704=812162300836, 705=813164300846, 706=814100342832, 707=814150042852, 708=814162342836, 709=815100425824, 710=815160025826, 711=815164005846, 712=817135003875, 713=817162002876, 714=820024131843, 715=823421314800, 716=823625300865, 717=823724300847, 718=824625141865, 719=824720041817, 720=825620035863, 721=825621415864, 722=825721315837, 723=825724005847, 724=827121400874, 725=827325131875, 726=827420034873, 727=827425004875, 728=830023421814, 729=830063121826, 730=831613002862, 731=831613400864, 732=834263241816, 733=834613142862, 734=834753141857, 735=835003425824, 736=835623425864, 737=835713125827, 738=837263200876, 739=837463004876, 740=840025421815, 741=840035423825, 742=840051412852, 743=840052432853, 744=841312432800, 745=841612432863, 746=841615400865, 747=842002431813, 748=842362431816, 749=842752400857, 750=845121425800, 751=845161425826, 752=845600435863, 753=845700425827, 754=847001412872, 755=847002432873, 756=847161400876, 757=847300432872, 758=847362432876, 759=850014152842, 760=850062352836, 761=850064151846, 762=851610052862, 763=851612452864, 764=851712352837, 765=852002451814, 766=852412154800, 767=852462354836, 768=852632453864, 769=853004352842, 770=853600352862, 771=853700351817, 772=857002452874, 773=857131453874, 774=857460054876, 775=860014136843, 776=860015126825, 777=860025326835, 778=860051416854, 779=861214236843, 780=861710026827, 781=861714006847, 782=862312136800, 783=862352436854, 784=862752006857, 785=863005326825, 786=863121326800, 787=863700326827, 788=863724326847, 789=863751316857, 790=864005346835, 791=864700346837, 792=864750046857, 793=867001416874, 794=867121426874, 795=867200236873, 796=867300436874, 797=867315136875, 798=890024121849, 799=891214200849, 800=891410024829, 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