The first 1124-sequence - Revision history

OBryant: /* Method */

2010-01-13T02:43:54Z

Method

← Older revision		Revision as of 19:43, 12 January 2010
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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 ==

Gowers: /* Links to other displays and visually displayed information about the sequence */

2010-01-11T15:22:40Z

Links to other displays and visually displayed information about the sequence

← Older revision		Revision as of 08:22, 11 January 2010
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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.

Gowers: /* Links to other displays and visually displayed information about the sequence */

2010-01-10T09:28:51Z

Links to other displays and visually displayed information about the sequence

← Older revision		Revision as of 02:28, 10 January 2010
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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].


	== 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.

OBryant: /* Status */ spelling fixes

2010-01-09T19:39:59Z

Status: spelling fixes

← Older revision		Revision as of 12:39, 9 January 2010
Line 12:		Line 12:
	== Status ==		== Status ==

	Is the data still relevant (e.g. longest ~~know~~)? Is the method still relevant, or have we found a better method? Is the program still running on a computer somewhere?		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~~ longest ~~know~~ sequence with discrepancy 2.		The sequence is a longest known sequence with discrepancy 2.

	== The data==		== The data==

SuneJ at 18:58, 9 January 2010

2010-01-09T18:58:31Z

← Older revision		Revision as of 11:58, 9 January 2010
Line 75:		Line 75:


	== ~~Relavant~~ 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.

SuneJ: /* Relavant Code */

2010-01-09T18:40:52Z

Relavant Code

← Older revision		Revision as of 11:40, 9 January 2010
Line 75:		Line 75:


	== Relavant ~~Code~~ ==		== Relavant 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.

SuneJ at 18:29, 9 January 2010

2010-01-09T18:29:00Z

← Older revision		Revision as of 11:29, 9 January 2010
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	The sequence is the longest know sequence with discrepancy 2.		The sequence is the longest know sequence with discrepancy 2.

			== The data==

	===The raw sequence===		===The raw sequence===

SuneJ: New page: 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. ==Multiplicati...

2010-01-09T18:14:33Z

New page: 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. ==Multiplicati...

New page

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 [http://gowers.wordpress.com/2009/12/17/erdoss-discrepancy-problem/#comment-4682 here] and [http://gowers.wordpress.com/2010/01/06/erdss-discrepancy-problem-as-a-forthcoming-polymath-project/#comment-4709 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.)

== Status ==

Is the data still relevant (e.g. longest know)? 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 longest know sequence with discrepancy 2.

===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. [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://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://thomas1111.wordpress.com/2010/01/09/erdos-discrepancy-a-program-to-get-html-tables/ 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: [http://obryant.wordpress.com/2010/01/09/a-rauzy-tree/ Link].

== Relavant Code ==
The code(s) (or a link to the code(s)) used to find this sequence should be posted here.