Identifier
Identifier
Values
0 => 2
1 => 3
00 => 4
01 => 5
10 => 6
11 => 7
000 => 8
001 => 9
010 => 10
011 => 11
100 => 12
101 => 13
110 => 14
111 => 15
0000 => 16
0001 => 17
0010 => 18
0011 => 19
0100 => 20
0101 => 21
0110 => 22
0111 => 23
1000 => 24
1001 => 25
1010 => 26
1011 => 27
1100 => 28
1101 => 29
1110 => 30
1111 => 31
00000 => 32
00001 => 33
00010 => 34
00011 => 35
00100 => 36
00101 => 37
00110 => 38
00111 => 39
01000 => 40
01001 => 41
01010 => 42
01011 => 43
01100 => 44
01101 => 45
01110 => 46
01111 => 47
10000 => 48
10001 => 49
10010 => 50
10011 => 51
10100 => 52
10101 => 53
10110 => 54
10111 => 55
11000 => 56
11001 => 57
11010 => 58
11011 => 59
11100 => 60
11101 => 61
11110 => 62
11111 => 63
000000 => 64
000001 => 65
000010 => 66
000011 => 67
000100 => 68
000101 => 69
000110 => 70
000111 => 71
001000 => 72
001001 => 73
001010 => 74
001011 => 75
001100 => 76
001101 => 77
001110 => 78
001111 => 79
010000 => 80
010001 => 81
010010 => 82
010011 => 83
010100 => 84
010101 => 85
010110 => 86
010111 => 87
011000 => 88
011001 => 89
011010 => 90
011011 => 91
011100 => 92
011101 => 93
011110 => 94
011111 => 95
100000 => 96
100001 => 97
100010 => 98
100011 => 99
100100 => 100
100101 => 101
100110 => 102
100111 => 103
101000 => 104
101001 => 105
101010 => 106
101011 => 107
101100 => 108
101101 => 109
101110 => 110
101111 => 111
110000 => 112
110001 => 113
110010 => 114
110011 => 115
110100 => 116
110101 => 117
110110 => 118
110111 => 119
111000 => 120
111001 => 121
111010 => 122
111011 => 123
111100 => 124
111101 => 125
111110 => 126
111111 => 127
0000000 => 128
0000001 => 129
0000010 => 130
0000011 => 131
0000100 => 132
0000101 => 133
0000110 => 134
0000111 => 135
0001000 => 136
0001001 => 137
0001010 => 138
0001011 => 139
0001100 => 140
0001101 => 141
0001110 => 142
0001111 => 143
0010000 => 144
0010001 => 145
0010010 => 146
0010011 => 147
0010100 => 148
0010101 => 149
0010110 => 150
0010111 => 151
0011000 => 152
0011001 => 153
0011010 => 154
0011011 => 155
0011100 => 156
0011101 => 157
0011110 => 158
0011111 => 159
0100000 => 160
0100001 => 161
0100010 => 162
0100011 => 163
0100100 => 164
0100101 => 165
0100110 => 166
0100111 => 167
0101000 => 168
0101001 => 169
0101010 => 170
0101011 => 171
0101100 => 172
0101101 => 173
0101110 => 174
0101111 => 175
0110000 => 176
0110001 => 177
0110010 => 178
0110011 => 179
0110100 => 180
0110101 => 181
0110110 => 182
0110111 => 183
0111000 => 184
0111001 => 185
0111010 => 186
0111011 => 187
0111100 => 188
0111101 => 189
0111110 => 190
0111111 => 191
1000000 => 192
1000001 => 193
1000010 => 194
1000011 => 195
1000100 => 196
1000101 => 197
1000110 => 198
1000111 => 199
1001000 => 200
1001001 => 201
1001010 => 202
1001011 => 203
1001100 => 204
1001101 => 205
1001110 => 206
1001111 => 207
1010000 => 208
1010001 => 209
1010010 => 210
1010011 => 211
1010100 => 212
1010101 => 213
1010110 => 214
1010111 => 215
1011000 => 216
1011001 => 217
1011010 => 218
1011011 => 219
1011100 => 220
1011101 => 221
1011110 => 222
1011111 => 223
1100000 => 224
1100001 => 225
1100010 => 226
1100011 => 227
1100100 => 228
1100101 => 229
1100110 => 230
1100111 => 231
1101000 => 232
1101001 => 233
1101010 => 234
1101011 => 235
1101100 => 236
1101101 => 237
1101110 => 238
1101111 => 239
1110000 => 240
1110001 => 241
1110010 => 242
1110011 => 243
1110100 => 244
1110101 => 245
1110110 => 246
1110111 => 247
1111000 => 248
1111001 => 249
1111010 => 250
1111011 => 251
1111100 => 252
1111101 => 253
1111110 => 254
1111111 => 255
00000000 => 256
00000001 => 257
00000010 => 258
00000011 => 259
00000100 => 260
00000101 => 261
00000110 => 262
00000111 => 263
00001000 => 264
00001001 => 265
00001010 => 266
00001011 => 267
00001100 => 268
00001101 => 269
00001110 => 270
00001111 => 271
00010000 => 272
00010001 => 273
00010010 => 274
00010011 => 275
00010100 => 276
00010101 => 277
00010110 => 278
00010111 => 279
00011000 => 280
00011001 => 281
00011010 => 282
00011011 => 283
00011100 => 284
00011101 => 285
00011110 => 286
00011111 => 287
00100000 => 288
00100001 => 289
00100010 => 290
00100011 => 291
00100100 => 292
00100101 => 293
00100110 => 294
00100111 => 295
00101000 => 296
00101001 => 297
00101010 => 298
00101011 => 299
00101100 => 300
00101101 => 301
00101110 => 302
00101111 => 303
00110000 => 304
00110001 => 305
00110010 => 306
00110011 => 307
00110100 => 308
00110101 => 309
00110110 => 310
00110111 => 311
00111000 => 312
00111001 => 313
00111010 => 314
00111011 => 315
00111100 => 316
00111101 => 317
00111110 => 318
00111111 => 319
01000000 => 320
01000001 => 321
01000010 => 322
01000011 => 323
01000100 => 324
01000101 => 325
01000110 => 326
01000111 => 327
01001000 => 328
01001001 => 329
01001010 => 330
01001011 => 331
01001100 => 332
01001101 => 333
01001110 => 334
01001111 => 335
01010000 => 336
01010001 => 337
01010010 => 338
01010011 => 339
01010100 => 340
01010101 => 341
01010110 => 342
01010111 => 343
01011000 => 344
01011001 => 345
01011010 => 346
01011011 => 347
01011100 => 348
01011101 => 349
01011110 => 350
01011111 => 351
01100000 => 352
01100001 => 353
01100010 => 354
01100011 => 355
01100100 => 356
01100101 => 357
01100110 => 358
01100111 => 359
01101000 => 360
01101001 => 361
01101010 => 362
01101011 => 363
01101100 => 364
01101101 => 365
01101110 => 366
01101111 => 367
01110000 => 368
01110001 => 369
01110010 => 370
01110011 => 371
01110100 => 372
01110101 => 373
01110110 => 374
01110111 => 375
01111000 => 376
01111001 => 377
01111010 => 378
01111011 => 379
01111100 => 380
01111101 => 381
01111110 => 382
01111111 => 383
10000000 => 384
10000001 => 385
10000010 => 386
10000011 => 387
10000100 => 388
10000101 => 389
10000110 => 390
10000111 => 391
10001000 => 392
10001001 => 393
10001010 => 394
10001011 => 395
10001100 => 396
10001101 => 397
10001110 => 398
10001111 => 399
10010000 => 400
10010001 => 401
10010010 => 402
10010011 => 403
10010100 => 404
10010101 => 405
10010110 => 406
10010111 => 407
10011000 => 408
10011001 => 409
10011010 => 410
10011011 => 411
10011100 => 412
10011101 => 413
10011110 => 414
10011111 => 415
10100000 => 416
10100001 => 417
10100010 => 418
10100011 => 419
10100100 => 420
10100101 => 421
10100110 => 422
10100111 => 423
10101000 => 424
10101001 => 425
10101010 => 426
10101011 => 427
10101100 => 428
10101101 => 429
10101110 => 430
10101111 => 431
10110000 => 432
10110001 => 433
10110010 => 434
10110011 => 435
10110100 => 436
10110101 => 437
10110110 => 438
10110111 => 439
10111000 => 440
10111001 => 441
10111010 => 442
10111011 => 443
10111100 => 444
10111101 => 445
10111110 => 446
10111111 => 447
11000000 => 448
11000001 => 449
11000010 => 450
11000011 => 451
11000100 => 452
11000101 => 453
11000110 => 454
11000111 => 455
11001000 => 456
11001001 => 457
11001010 => 458
11001011 => 459
11001100 => 460
11001101 => 461
11001110 => 462
11001111 => 463
11010000 => 464
11010001 => 465
11010010 => 466
11010011 => 467
11010100 => 468
11010101 => 469
11010110 => 470
11010111 => 471
11011000 => 472
11011001 => 473
11011010 => 474
11011011 => 475
11011100 => 476
11011101 => 477
11011110 => 478
11011111 => 479
11100000 => 480
11100001 => 481
11100010 => 482
11100011 => 483
11100100 => 484
11100101 => 485
11100110 => 486
11100111 => 487
11101000 => 488
11101001 => 489
11101010 => 490
11101011 => 491
11101100 => 492
11101101 => 493
11101110 => 494
11101111 => 495
11110000 => 496
11110001 => 497
11110010 => 498
11110011 => 499
11110100 => 500
11110101 => 501
11110110 => 502
11110111 => 503
11111000 => 504
11111001 => 505
11111010 => 506
11111011 => 507
11111100 => 508
11111101 => 509
11111110 => 510
11111111 => 511
000000000 => 512
000000001 => 513
000000010 => 514
000000011 => 515
000000100 => 516
000000101 => 517
000000110 => 518
000000111 => 519
000001000 => 520
000001001 => 521
000001010 => 522
000001011 => 523
000001100 => 524
000001101 => 525
000001110 => 526
000001111 => 527
000010000 => 528
000010001 => 529
000010010 => 530
000010011 => 531
000010100 => 532
000010101 => 533
000010110 => 534
000010111 => 535
000011000 => 536
000011001 => 537
000011010 => 538
000011011 => 539
000011100 => 540
000011101 => 541
000011110 => 542
000011111 => 543
000100000 => 544
000100001 => 545
000100010 => 546
000100011 => 547
000100100 => 548
000100101 => 549
000100110 => 550
000100111 => 551
000101000 => 552
000101001 => 553
000101010 => 554
000101011 => 555
000101100 => 556
000101101 => 557
000101110 => 558
000101111 => 559
000110000 => 560
000110001 => 561
000110010 => 562
000110011 => 563
000110100 => 564
000110101 => 565
000110110 => 566
000110111 => 567
000111000 => 568
000111001 => 569
000111010 => 570
000111011 => 571
000111100 => 572
000111101 => 573
000111110 => 574
000111111 => 575
001000000 => 576
001000001 => 577
001000010 => 578
001000011 => 579
001000100 => 580
001000101 => 581
001000110 => 582
001000111 => 583
001001000 => 584
001001001 => 585
001001010 => 586
001001011 => 587
001001100 => 588
001001101 => 589
001001110 => 590
001001111 => 591
001010000 => 592
001010001 => 593
001010010 => 594
001010011 => 595
001010100 => 596
001010101 => 597
001010110 => 598
001010111 => 599
001011000 => 600
001011001 => 601
001011010 => 602
001011011 => 603
001011100 => 604
001011101 => 605
001011110 => 606
001011111 => 607
001100000 => 608
001100001 => 609
001100010 => 610
001100011 => 611
001100100 => 612
001100101 => 613
001100110 => 614
001100111 => 615
001101000 => 616
001101001 => 617
001101010 => 618
001101011 => 619
001101100 => 620
001101101 => 621
001101110 => 622
001101111 => 623
001110000 => 624
001110001 => 625
001110010 => 626
001110011 => 627
001110100 => 628
001110101 => 629
001110110 => 630
001110111 => 631
001111000 => 632
001111001 => 633
001111010 => 634
001111011 => 635
001111100 => 636
001111101 => 637
001111110 => 638
001111111 => 639
010000000 => 640
010000001 => 641
010000010 => 642
010000011 => 643
010000100 => 644
010000101 => 645
010000110 => 646
010000111 => 647
010001000 => 648
010001001 => 649
010001010 => 650
010001011 => 651
010001100 => 652
010001101 => 653
010001110 => 654
010001111 => 655
010010000 => 656
010010001 => 657
010010010 => 658
010010011 => 659
010010100 => 660
010010101 => 661
010010110 => 662
010010111 => 663
010011000 => 664
010011001 => 665
010011010 => 666
010011011 => 667
010011100 => 668
010011101 => 669
010011110 => 670
010011111 => 671
010100000 => 672
010100001 => 673
010100010 => 674
010100011 => 675
010100100 => 676
010100101 => 677
010100110 => 678
010100111 => 679
010101000 => 680
010101001 => 681
010101010 => 682
010101011 => 683
010101100 => 684
010101101 => 685
010101110 => 686
010101111 => 687
010110000 => 688
010110001 => 689
010110010 => 690
010110011 => 691
010110100 => 692
010110101 => 693
010110110 => 694
010110111 => 695
010111000 => 696
010111001 => 697
010111010 => 698
010111011 => 699
010111100 => 700
010111101 => 701
010111110 => 702
010111111 => 703
011000000 => 704
011000001 => 705
011000010 => 706
011000011 => 707
011000100 => 708
011000101 => 709
011000110 => 710
011000111 => 711
011001000 => 712
011001001 => 713
011001010 => 714
011001011 => 715
011001100 => 716
011001101 => 717
011001110 => 718
011001111 => 719
011010000 => 720
011010001 => 721
011010010 => 722
011010011 => 723
011010100 => 724
011010101 => 725
011010110 => 726
011010111 => 727
011011000 => 728
011011001 => 729
011011010 => 730
011011011 => 731
011011100 => 732
011011101 => 733
011011110 => 734
011011111 => 735
011100000 => 736
011100001 => 737
011100010 => 738
011100011 => 739
011100100 => 740
011100101 => 741
011100110 => 742
011100111 => 743
011101000 => 744
011101001 => 745
011101010 => 746
011101011 => 747
011101100 => 748
011101101 => 749
011101110 => 750
011101111 => 751
011110000 => 752
011110001 => 753
011110010 => 754
011110011 => 755
011110100 => 756
011110101 => 757
011110110 => 758
011110111 => 759
011111000 => 760
011111001 => 761
011111010 => 762
011111011 => 763
011111100 => 764
011111101 => 765
011111110 => 766
011111111 => 767
100000000 => 768
100000001 => 769
100000010 => 770
100000011 => 771
100000100 => 772
100000101 => 773
100000110 => 774
100000111 => 775
100001000 => 776
100001001 => 777
100001010 => 778
100001011 => 779
100001100 => 780
100001101 => 781
100001110 => 782
100001111 => 783
100010000 => 784
100010001 => 785
100010010 => 786
100010011 => 787
100010100 => 788
100010101 => 789
100010110 => 790
100010111 => 791
100011000 => 792
100011001 => 793
100011010 => 794
100011011 => 795
100011100 => 796
100011101 => 797
100011110 => 798
100011111 => 799
100100000 => 800
100100001 => 801
100100010 => 802
100100011 => 803
100100100 => 804
100100101 => 805
100100110 => 806
100100111 => 807
100101000 => 808
100101001 => 809
100101010 => 810
100101011 => 811
100101100 => 812
100101101 => 813
100101110 => 814
100101111 => 815
100110000 => 816
100110001 => 817
100110010 => 818
100110011 => 819
100110100 => 820
100110101 => 821
100110110 => 822
100110111 => 823
100111000 => 824
100111001 => 825
100111010 => 826
100111011 => 827
100111100 => 828
100111101 => 829
100111110 => 830
100111111 => 831
101000000 => 832
101000001 => 833
101000010 => 834
101000011 => 835
101000100 => 836
101000101 => 837
101000110 => 838
101000111 => 839
101001000 => 840
101001001 => 841
101001010 => 842
101001011 => 843
101001100 => 844
101001101 => 845
101001110 => 846
101001111 => 847
101010000 => 848
101010001 => 849
101010010 => 850
101010011 => 851
101010100 => 852
101010101 => 853
101010110 => 854
101010111 => 855
101011000 => 856
101011001 => 857
101011010 => 858
101011011 => 859
101011100 => 860
101011101 => 861
101011110 => 862
101011111 => 863
101100000 => 864
101100001 => 865
101100010 => 866
101100011 => 867
101100100 => 868
101100101 => 869
101100110 => 870
101100111 => 871
101101000 => 872
101101001 => 873
101101010 => 874
101101011 => 875
101101100 => 876
101101101 => 877
101101110 => 878
101101111 => 879
101110000 => 880
101110001 => 881
101110010 => 882
101110011 => 883
101110100 => 884
101110101 => 885
101110110 => 886
101110111 => 887
101111000 => 888
101111001 => 889
101111010 => 890
101111011 => 891
101111100 => 892
101111101 => 893
101111110 => 894
101111111 => 895
110000000 => 896
110000001 => 897
110000010 => 898
110000011 => 899
110000100 => 900
110000101 => 901
110000110 => 902
110000111 => 903
110001000 => 904
110001001 => 905
110001010 => 906
110001011 => 907
110001100 => 908
110001101 => 909
110001110 => 910
110001111 => 911
110010000 => 912
110010001 => 913
110010010 => 914
110010011 => 915
110010100 => 916
110010101 => 917
110010110 => 918
110010111 => 919
110011000 => 920
110011001 => 921
110011010 => 922
110011011 => 923
110011100 => 924
110011101 => 925
110011110 => 926
110011111 => 927
110100000 => 928
110100001 => 929
110100010 => 930
110100011 => 931
110100100 => 932
110100101 => 933
110100110 => 934
110100111 => 935
110101000 => 936
110101001 => 937
110101010 => 938
110101011 => 939
110101100 => 940
110101101 => 941
110101110 => 942
110101111 => 943
110110000 => 944
110110001 => 945
110110010 => 946
110110011 => 947
110110100 => 948
110110101 => 949
110110110 => 950
110110111 => 951
110111000 => 952
110111001 => 953
110111010 => 954
110111011 => 955
110111100 => 956
110111101 => 957
110111110 => 958
110111111 => 959
111000000 => 960
111000001 => 961
111000010 => 962
111000011 => 963
111000100 => 964
111000101 => 965
111000110 => 966
111000111 => 967
111001000 => 968
111001001 => 969
111001010 => 970
111001011 => 971
111001100 => 972
111001101 => 973
111001110 => 974
111001111 => 975
111010000 => 976
111010001 => 977
111010010 => 978
111010011 => 979
111010100 => 980
111010101 => 981
111010110 => 982
111010111 => 983
111011000 => 984
111011001 => 985
111011010 => 986
111011011 => 987
111011100 => 988
111011101 => 989
111011110 => 990
111011111 => 991
111100000 => 992
111100001 => 993
111100010 => 994
111100011 => 995
111100100 => 996
111100101 => 997
111100110 => 998
111100111 => 999
111101000 => 1000
111101001 => 1001
111101010 => 1002
111101011 => 1003
111101100 => 1004
111101101 => 1005
111101110 => 1006
111101111 => 1007
111110000 => 1008
111110001 => 1009
111110010 => 1010
111110011 => 1011
111110100 => 1012
111110101 => 1013
111110110 => 1014
111110111 => 1015
111111000 => 1016
111111001 => 1017
111111010 => 1018
111111011 => 1019
111111100 => 1020
111111101 => 1021
111111110 => 1022
111111111 => 1023
0000000000 => 1024
0000000001 => 1025
0000000010 => 1026
0000000011 => 1027
0000000100 => 1028
0000000101 => 1029
0000000110 => 1030
0000000111 => 1031
0000001000 => 1032
0000001001 => 1033
0000001010 => 1034
0000001011 => 1035
0000001100 => 1036
0000001101 => 1037
0000001110 => 1038
0000001111 => 1039
0000010000 => 1040
0000010001 => 1041
0000010010 => 1042
0000010011 => 1043
0000010100 => 1044
0000010101 => 1045
0000010110 => 1046
0000010111 => 1047
0000011000 => 1048
0000011001 => 1049
0000011010 => 1050
0000011011 => 1051
0000011100 => 1052
0000011101 => 1053
0000011110 => 1054
0000011111 => 1055
0000100000 => 1056
0000100001 => 1057
0000100010 => 1058
0000100011 => 1059
0000100100 => 1060
0000100101 => 1061
0000100110 => 1062
0000100111 => 1063
0000101000 => 1064
0000101001 => 1065
0000101010 => 1066
0000101011 => 1067
0000101100 => 1068
0000101101 => 1069
0000101110 => 1070
0000101111 => 1071
0000110000 => 1072
0000110001 => 1073
0000110010 => 1074
0000110011 => 1075
0000110100 => 1076
0000110101 => 1077
0000110110 => 1078
0000110111 => 1079
0000111000 => 1080
0000111001 => 1081
0000111010 => 1082
0000111011 => 1083
0000111100 => 1084
0000111101 => 1085
0000111110 => 1086
0000111111 => 1087
0001000000 => 1088
0001000001 => 1089
0001000010 => 1090
0001000011 => 1091
0001000100 => 1092
0001000101 => 1093
0001000110 => 1094
0001000111 => 1095
0001001000 => 1096
0001001001 => 1097
0001001010 => 1098
0001001011 => 1099
0001001100 => 1100
0001001101 => 1101
0001001110 => 1102
0001001111 => 1103
0001010000 => 1104
0001010001 => 1105
0001010010 => 1106
0001010011 => 1107
0001010100 => 1108
0001010101 => 1109
0001010110 => 1110
0001010111 => 1111
0001011000 => 1112
0001011001 => 1113
0001011010 => 1114
0001011011 => 1115
0001011100 => 1116
0001011101 => 1117
0001011110 => 1118
0001011111 => 1119
0001100000 => 1120
0001100001 => 1121
0001100010 => 1122
0001100011 => 1123
0001100100 => 1124
0001100101 => 1125
0001100110 => 1126
0001100111 => 1127
0001101000 => 1128
0001101001 => 1129
0001101010 => 1130
0001101011 => 1131
0001101100 => 1132
0001101101 => 1133
0001101110 => 1134
0001101111 => 1135
0001110000 => 1136
0001110001 => 1137
0001110010 => 1138
0001110011 => 1139
0001110100 => 1140
0001110101 => 1141
0001110110 => 1142
0001110111 => 1143
0001111000 => 1144
0001111001 => 1145
0001111010 => 1146
0001111011 => 1147
0001111100 => 1148
0001111101 => 1149
0001111110 => 1150
0001111111 => 1151
0010000000 => 1152
0010000001 => 1153
0010000010 => 1154
0010000011 => 1155
0010000100 => 1156
0010000101 => 1157
0010000110 => 1158
0010000111 => 1159
0010001000 => 1160
0010001001 => 1161
0010001010 => 1162
0010001011 => 1163
0010001100 => 1164
0010001101 => 1165
0010001110 => 1166
0010001111 => 1167
0010010000 => 1168
0010010001 => 1169
0010010010 => 1170
0010010011 => 1171
0010010100 => 1172
0010010101 => 1173
0010010110 => 1174
0010010111 => 1175
0010011000 => 1176
0010011001 => 1177
0010011010 => 1178
0010011011 => 1179
0010011100 => 1180
0010011101 => 1181
0010011110 => 1182
0010011111 => 1183
0010100000 => 1184
0010100001 => 1185
0010100010 => 1186
0010100011 => 1187
0010100100 => 1188
0010100101 => 1189
0010100110 => 1190
0010100111 => 1191
0010101000 => 1192
0010101001 => 1193
0010101010 => 1194
0010101011 => 1195
0010101100 => 1196
0010101101 => 1197
0010101110 => 1198
0010101111 => 1199
0010110000 => 1200
0010110001 => 1201
click to show generating function       
Description
The decimal representation of a binary word with a leading 1.
This statistic is obtained by prepending $1$ to the binary word and interpreting it as a number in binary.
Code
def statistic(w):
    return Integer("0b1" + str(w))

Created
May 30, 2017 at 21:43 by Martin Rubey
Updated
May 30, 2017 at 21:43 by Martin Rubey