The first 1124-sequence: Difference between revisions
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==Method== | ==Method== | ||
Here should be a short description of the way the sequence was found. (The code(s) used should be further down this page.) | Here should be a short description of the way the sequence was found. (The code(s) used should be further down this page.) [Is this the lexicographically last example?] | ||
== Status == | == Status == | ||
Is the data still relevant (e.g. longest | Is the data still relevant (e.g. longest known)? Is the method still relevant, or have we found a better method? Is the program still running on a computer somewhere? | ||
The sequence is | The sequence is a longest known sequence with discrepancy 2. | ||
== The data== | == The data== | ||
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Here is an alternate formatting. [http://numberwarrior.wordpress.com/files/2009/12/longsequence.png Link]. | Here is an alternate formatting. [http://numberwarrior.wordpress.com/files/2009/12/longsequence.png Link]. | ||
[http://spreadsheets.google.com/ccc?key=0AkbsKAn5VTtvdGpoOG9xYWlUYTNpa1I0UktEMUsxZmc&hl=en The sequence in groups of 24] (Google Docs format). | [http://spreadsheets.google.com/ccc?key=0AkbsKAn5VTtvdGpoOG9xYWlUYTNpa1I0UktEMUsxZmc&hl=en The sequence in groups of 24 and in colour] (Google Docs format). | ||
[http://go2.wordpress.com/?id=725X1342&site=gowers.wordpress.com&url=http%3A%2F%2Fspreadsheets.google.com%2Fccc%3Fkey%3D0AkbsKAn5VTtvdDdrTDd1YmM3bGZESEFwZWhnSVBZMEE%26hl%3Den Multiples of 2 only]. | [http://go2.wordpress.com/?id=725X1342&site=gowers.wordpress.com&url=http%3A%2F%2Fspreadsheets.google.com%2Fccc%3Fkey%3D0AkbsKAn5VTtvdDdrTDd1YmM3bGZESEFwZWhnSVBZMEE%26hl%3Den Multiples of 2 only]. | ||
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Here is a Rauzy tree that conveys information about subsequences of the sequence: [http://obryant.wordpress.com/2010/01/09/a-rauzy-tree/ Link]. | Here is a Rauzy tree that conveys information about subsequences of the sequence: [http://obryant.wordpress.com/2010/01/09/a-rauzy-tree/ Link]. | ||
The HAP-subsequences of the sequence are tabulated [http://thomas1111.wordpress.com/2010/01/09/erdos-discrepancy-a-program-to-get-html-tables/ at the bottom of this page], making them very easy to compare and contrast with one another. | |||
== Relevant code == | == Relevant code == | ||
The code(s) (or a link to the code(s)) used to find this sequence should be posted here. | The code(s) (or a link to the code(s)) used to find this sequence should be posted here. | ||
Latest revision as of 18:43, 12 January 2010
This is a sequence with 1124 terms and discrepancy 2. We haven't found any longer sequences with discrepancy 2, but we have found more than 400 000 000 with this length.
Multiplicativity properties of the 1124 sequence
The 1124 sequence is not weakly multiplicative, but it does appear to be close to a weakly multiplicative sequence. That is, if you are prepared to disregard a few "errors", then the number of distinct HAP-subsequences is 6. One can use this information to identify a quasi-multiplicative sequence that is in some sense close to the 1124 sequence. Some details can be found in the sequences of comments that begin here and here.
Method
Here should be a short description of the way the sequence was found. (The code(s) used should be further down this page.) [Is this the lexicographically last example?]
Status
Is the data still relevant (e.g. longest known)? Is the method still relevant, or have we found a better method? Is the program still running on a computer somewhere?
The sequence is a longest known sequence with discrepancy 2.
The data
The raw sequence
+ - + + - - - - + + - + + + - - + - + + - - - + - + + - + - - + + - + - - + - - + + - + + - - - + + + - - + - + - - + + + + - - + - - + + - - + + + - - + + - + - - + - - + + - + - - + - + + + - - + - + - - + + - - - + + - + + + - - - + - - + - + + + + - - - - + + - + + + - - + - - + - - + - + - + + - + + + - - - - + + + + - - - + + - + - - + - + + - - + - + + - + - + - + + - - - + + - + + - - + - - + - - + + + + - + - - + - - + + - - + - + + - - - + - + + - + + + - - + + - - + - - + - + + - - + - + + - + + - - + - - + - + + - - + + - + - + - - + - + + + - - + - + + - - - - + + - - + - + + - + + - - + - + + - - + + - + - - + - + - - + + - - + - + + + - + - - + - + - - + + + + - - - + + - + - - + - + + - - + - + + - + + - - + - - + - + + - - + + - - - + + - - + - + + - + + - - + - - + + + + - - - - + + - + + - + + - - + - - + + - - - + + - + + - - + - + + - + - - - + - + + - + + - - + - - + - + + - - + + - + + + - - - + - + + - + + - - + - - - + + + - - + - + - - + + + - + - + + - + - - - + + - + - + + - - + - - + - + + - - + - + - + + - + - + - - + - + + - - + - - + - + + + - - - + + - + + + - + - - + - + + - - + - + + - + - - - + - + + - + + - - + - - - + + + - - + - + + - - + + - + - + + - + - - - + - - + - + + - - + - + + - + + - - + - + + - + + - - + - - + - + + - - + - - + - + + - + - - + + - + + - - + - - + - + + - - + - + + - + + - - + - + + - - + + - + - - + - + + - - + - - + - + + - - + - + + - + + - + + - - + - + + - - + - - + - + + - - + - + - - + + + - + - - + - + + - - + - + - - + + + - - - + + - + + - - + + - + - + + - - + - - + - - + - + + - + - - + + + - + - - + - + + - - + - + - - + + - - + - + + - + + - - + + - + - - + - - + - + + - + + - - + - + + - + + - - + - - + + + - - - + - - + - + + - - + + + + - + - - + + - - + - + + - - + - - + - + + - - + - + + - + + - - + - - + - + + - - - + + - - + + - - + - + + - + + - - + - - + - + + + - + - - + - + + - - + - + + - + - + - - + - + - + + - - + - + - - + + + - + - - - + + + - - + - - + - + + - - + + + + - + - - - + - + + - + + - - + - - + + + - - - + - - + - + + + - + - + + - + - - - + - - + + + + - - + - + + - - + - + + - + - - + - + + - - - + - - + + - + - + + - + - - - + - + + + + - + - - - - + - + + - + + - - + + - + + - + - - + - + + - + - -
The sequence, together with the corresponding integers
1+ 2- 3+ 4+ 5- 6- 7- 8- 9+ 10+ 11- 12+ 13+ 14+ 15- 16- 17+ 18- 19+ 20+ 21- 22- 23- 24+ 25- 26+ 27+ 28- 29+ 30- 31- 32+ 33+ 34- 35+ 36- 37- 38+ 39- 40- 41+ 42+ 43- 44+ 45+ 46- 47- 48- 49+ 50+ 51+ 52- 53- 54+ 55- 56+ 57- 58- 59+ 60+ 61+ 62+ 63- 64- 65+ 66- 67- 68+ 69+ 70- 71- 72+ 73+ 74+ 75- 76- 77+ 78+ 79- 80+ 81- 82- 83+ 84- 85- 86+ 87+ 88- 89+ 90- 91- 92+ 93- 94+ 95+ 96+ 97- 98- 99+ 100- 101+ 102- 103- 104+ 105+ 106- 107- 108- 109+ 110+ 111- 112+ 113+ 114+ 115- 116- 117- 118+ 119- 120- 121+ 122- 123+ 124+ 125+ 126+ 127- 128- 129- 130- 131+ 132+ 133- 134+ 135+ 136+ 137- 138- 139+ 140- 141- 142+ 143- 144- 145+ 146- 147+ 148- 149+ 150+ 151- 152+ 153+ 154+ 155- 156- 157- 158- 159+ 160+ 161+ 162+ 163- 164- 165- 166+ 167+ 168- 169+ 170- 171- 172+ 173- 174+ 175+ 176- 177- 178+ 179- 180+ 181+ 182- 183+ 184- 185+ 186- 187+ 188+ 189- 190- 191- 192+ 193+ 194- 195+ 196+ 197- 198- 199+ 200- 201- 202+ 203- 204- 205+ 206+ 207+ 208+ 209- 210+ 211- 212- 213+ 214- 215- 216+ 217+ 218- 219- 220+ 221- 222+ 223+ 224- 225- 226- 227+ 228- 229+ 230+ 231- 232+ 233+ 234+ 235- 236- 237+ 238+ 239- 240- 241+ 242- 243- 244+ 245- 246+ 247+ 248- 249- 250+ 251- 252+ 253+ 254- 255+ 256+ 257- 258- 259+ 260- 261- 262+ 263- 264+ 265+ 266- 267- 268+ 269+ 270- 271+ 272- 273+ 274- 275- 276+ 277- 278+ 279+ 280+ 281- 282- 283+ 284- 285+ 286+ 287- 288- 289- 290- 291+ 292+ 293- 294- 295+ 296- 297+ 298+ 299- 300+ 301+ 302- 303- 304+ 305- 306+ 307+ 308- 309- 310+ 311+ 312- 313+ 314- 315- 316+ 317- 318+ 319- 320- 321+ 322+ 323- 324- 325+ 326- 327+ 328+ 329+ 330- 331+ 332- 333- 334+ 335- 336+ 337- 338- 339+ 340+ 341+ 342+ 343- 344- 345- 346+ 347+ 348- 349+ 350- 351- 352+ 353- 354+ 355+ 356- 357- 358+ 359- 360+ 361+ 362- 363+ 364+ 365- 366- 367+ 368- 369- 370+ 371- 372+ 373+ 374- 375- 376+ 377+ 378- 379- 380- 381+ 382+ 383- 384- 385+ 386- 387+ 388+ 389- 390+ 391+ 392- 393- 394+ 395- 396- 397+ 398+ 399+ 400+ 401- 402- 403- 404- 405+ 406+ 407- 408+ 409+ 410- 411+ 412+ 413- 414- 415+ 416- 417- 418+ 419+ 420- 421- 422- 423+ 424+ 425- 426+ 427+ 428- 429- 430+ 431- 432+ 433+ 434- 435+ 436- 437- 438- 439+ 440- 441+ 442+ 443- 444+ 445+ 446- 447- 448+ 449- 450- 451+ 452- 453+ 454+ 455- 456- 457+ 458+ 459- 460+ 461+ 462+ 463- 464- 465- 466+ 467- 468+ 469+ 470- 471+ 472+ 473- 474- 475+ 476- 477- 478- 479+ 480+ 481+ 482- 483- 484+ 485- 486+ 487- 488- 489+ 490+ 491+ 492- 493+ 494- 495+ 496+ 497- 498+ 499- 500- 501- 502+ 503+ 504- 505+ 506- 507+ 508+ 509- 510- 511+ 512- 513- 514+ 515- 516+ 517+ 518- 519- 520+ 521- 522+ 523- 524+ 525+ 526- 527+ 528- 529+ 530- 531- 532+ 533- 534+ 535+ 536- 537- 538+ 539- 540- 541+ 542- 543+ 544+ 545+ 546- 547- 548- 549+ 550+ 551- 552+ 553+ 554+ 555- 556+ 557- 558- 559+ 560- 561+ 562+ 563- 564- 565+ 566- 567+ 568+ 569- 570+ 571- 572- 573- 574+ 575- 576+ 577+ 578- 579+ 580+ 581- 582- 583+ 584- 585- 586- 587+ 588+ 589+ 590- 591- 592+ 593- 594+ 595+ 596- 597- 598+ 599+ 600- 601+ 602- 603+ 604+ 605- 606+ 607- 608- 609- 610+ 611- 612- 613+ 614- 615+ 616+ 617- 618- 619+ 620- 621+ 622+ 623- 624+ 625+ 626- 627- 628+ 629- 630+ 631+ 632- 633+ 634+ 635- 636- 637+ 638- 639- 640+ 641- 642+ 643+ 644- 645- 646+ 647- 648- 649+ 650- 651+ 652+ 653- 654+ 655- 656- 657+ 658+ 659- 660+ 661+ 662- 663- 664+ 665- 666- 667+ 668- 669+ 670+ 671- 672- 673+ 674- 675+ 676+ 677- 678+ 679+ 680- 681- 682+ 683- 684+ 685+ 686- 687- 688+ 689+ 690- 691+ 692- 693- 694+ 695- 696+ 697+ 698- 699- 700+ 701- 702- 703+ 704- 705+ 706+ 707- 708- 709+ 710- 711+ 712+ 713- 714+ 715+ 716- 717+ 718+ 719- 720- 721+ 722- 723+ 724+ 725- 726- 727+ 728- 729- 730+ 731- 732+ 733+ 734- 735- 736+ 737- 738+ 739- 740- 741+ 742+ 743+ 744- 745+ 746- 747- 748+ 749- 750+ 751+ 752- 753- 754+ 755- 756+ 757- 758- 759+ 760+ 761+ 762- 763- 764- 765+ 766+ 767- 768+ 769+ 770- 771- 772+ 773+ 774- 775+ 776- 777+ 778+ 779- 780- 781+ 782- 783- 784+ 785- 786- 787+ 788- 789+ 790+ 791- 792+ 793- 794- 795+ 796+ 797+ 798- 799+ 800- 801- 802+ 803- 804+ 805+ 806- 807- 808+ 809- 810+ 811- 812- 813+ 814+ 815- 816- 817+ 818- 819+ 820+ 821- 822+ 823+ 824- 825- 826+ 827+ 828- 829+ 830- 831- 832+ 833- 834- 835+ 836- 837+ 838+ 839- 840+ 841+ 842- 843- 844+ 845- 846+ 847+ 848- 849+ 850+ 851- 852- 853+ 854- 855- 856+ 857+ 858+ 859- 860- 861- 862+ 863- 864- 865+ 866- 867+ 868+ 869- 870- 871+ 872+ 873+ 874+ 875- 876+ 877- 878- 879+ 880+ 881- 882- 883+ 884- 885+ 886+ 887- 888- 889+ 890- 891- 892+ 893- 894+ 895+ 896- 897- 898+ 899- 900+ 901+ 902- 903+ 904+ 905- 906- 907+ 908- 909- 910+ 911- 912+ 913+ 914- 915- 916- 917+ 918+ 919- 920- 921+ 922+ 923- 924- 925+ 926- 927+ 928+ 929- 930+ 931+ 932- 933- 934+ 935- 936- 937+ 938- 939+ 940+ 941+ 942- 943+ 944- 945- 946+ 947- 948+ 949+ 950- 951- 952+ 953- 954+ 955+ 956- 957+ 958- 959+ 960- 961- 962+ 963- 964+ 965- 966+ 967+ 968- 969- 970+ 971- 972+ 973- 974- 975+ 976+ 977+ 978- 979+ 980- 981- 982- 983+ 984+ 985+ 986- 987- 988+ 989- 990- 991+ 992- 993+ 994+ 995- 996- 997+ 998+ 999+ 1000+ 1001- 1002+ 1003- 1004- 1005- 1006+ 1007- 1008+ 1009+ 1010- 1011+ 1012+ 1013- 1014- 1015+ 1016- 1017- 1018+ 1019+ 1020+ 1021- 1022- 1023- 1024+ 1025- 1026- 1027+ 1028- 1029+ 1030+ 1031+ 1032- 1033+ 1034- 1035+ 1036+ 1037- 1038+ 1039- 1040- 1041- 1042+ 1043- 1044- 1045+ 1046+ 1047+ 1048+ 1049- 1050- 1051+ 1052- 1053+ 1054+ 1055- 1056- 1057+ 1058- 1059+ 1060+ 1061- 1062+ 1063- 1064- 1065+ 1066- 1067+ 1068+ 1069- 1070- 1071- 1072+ 1073- 1074- 1075+ 1076+ 1077- 1078+ 1079- 1080+ 1081+ 1082- 1083+ 1084- 1085- 1086- 1087+ 1088- 1089+ 1090+ 1091+ 1092+ 1093- 1094+ 1095- 1096- 1097- 1098- 1099+ 1100- 1101+ 1102+ 1103- 1104+ 1105+ 1106- 1107- 1108+ 1109+ 1110- 1111+ 1112+ 1113- 1114+ 1115- 1116- 1117+ 1118- 1119+ 1120+ 1121- 1122+ 1123- 1124-
Links to other displays and visually displayed information about the sequence
Here is an alternate formatting. Link.
The sequence in groups of 24 and in colour (Google Docs format). Multiples of 2 only.
The sequence in groups of 24, also multiples of 8 only (HTML format).
Here is a Rauzy tree that conveys information about subsequences of the sequence: Link.
The HAP-subsequences of the sequence are tabulated at the bottom of this page, making them very easy to compare and contrast with one another.
Relevant code
The code(s) (or a link to the code(s)) used to find this sequence should be posted here.
