Early Bird numbers

[Maximilian Hasler]

at the second glance, I take back my premature proposal concerning a
"late bird" conjecture - as shows the following PHP 1-liner,

Late birds:
<?php $s="."; for(; ++$i < 2000; $s .= $i) if( !strpos($s,"$i")) echo $i,", ";

there are many late birds in the "1xxxx" range for any number of digits.
Sorry...
M.H.

Late birds:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 22,
24, 25, 26, 27, 28, 29, 30, 33, 35, 36, 37, 38, 39, 40, 44, 46, 47,
48, 49, 50, 55, 57, 58, 59, 60, 66, 68, 69, 70, 77, 79, 80, 88, 90,
100, 102, 103, 104, 105, 106, 107, 108, 109, 113, 114, 115, 116, 117,
118, 119, 120, 124, 125, 126, 127, 128, 129, 130, 133, 134, 135, 136,
137, 138, 139, 140, 143, 144, 145, 146, 147, 148, 149, 150, 153, 154,
155, 156, 157, 158, 159, 160, 163, 164, 165, 166, 167, 168, 169, 170,
173, 174, 175, 176, 177, 178, 179, 180, 183, 184, 185, 186, 187, 188,
189, 190, 193, 194, 195, 196, 197, 198, 199, 200, 203, 204, 205, 206,
207, 208, 209, 224, 225, 226, 227, 228, 229, 230, 235, 236, 237, 238,
239, 240, 244, 245, 246, 247, 248, 249, 250, 254, 255, 256, 257, 258,
259, 260, 264, 265, 266, 267, 268, 269, 270, 274, 275, 276, 277, 278,
279, 280, 284, 285, 286, 287, 288, 289, 290, 294, 295, 296, 297, 298,
299, 300, 304, 305, 306, 307, 308, 309, 335, 336, 337, 338, 339, 340,
346, 347, 348, 349, 350, 355, 356, 357, 358, 359, 360, 365, 366, 367,
368, 369, 370, 375, 376, 377, 378, 379, 380, 385, 386, 387, 388, 389,
390, 395, 396, 397, 398, 399, 400, 405, 406, 407, 408, 409, 446, 447,
448, 449, 450, 457, 458, 459, 460, 466, 467, 468, 469, 470, 476, 477,
478, 479, 480, 486, 487, 488, 489, 490, 496, 497, 498, 499, 500, 506,
507, 508, 509, 557, 558, 559, 560, 568, 569, 570, 577, 578, 579, 580,
587, 588, 589, 590, 597, 598, 599, 600, 607, 608, 609, 668, 669, 670,
679, 680, 688, 689, 690, 698, 699, 700, 708, 709, 779, 780, 790, 799,
800, 809, 890, 900, 1000, 1002, 1003, 1004, 1005, 1006, 1007, 1008,
1009, 1010, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020,
1022, 1023, ...

On 7/23/07, Maximilian Hasler <maximilian.hasler at gmail.com> wrote:
> This is another example of how computers can denature things.
> "Early birds" seem interesting when you do it by hand, for n<199, say
> ; but from then on it would be more interesting to study the
> complementary sequence ("late birds" ? which appear not before their
> "regular" place) - e.g. among 500..999 only about 50 terms are not
> present.
> At a first glance, I'd almost be tempted to conjecture that from a
> certain rank on, the only late birds are of the form  d*10^k with d in
> {1,...,9 }, and all other numbers are early birds...
> M.H.
>
> On 7/23/07, Joshua Zucker <joshua.zucker at gmail.com> wrote:
> > I wrote my own program and let it run to make all the terms up to
> > 1000.  Up to 394 they match the terms Warut's program produced.
> >
> > --Joshua Zucker
> >
> > 12 21 23 31 32 34 41 42 43 45 51 52 53 54 56 61 62 63 64 65 67 71 72
> > 73 74 75 76 78 81 82 83 84 85 86 87 89 91 92 93 94 95 96 97 98 99 101
> > 110 111 112 121 122 123 131 132 141 142 151 152 161 162 171 172 181
> > 182 191 192 201 202 210 211 212 213 214 215 216 217 218 219 220 221
> > 222 223 231 232 233 234 241 242 243 251 252 253 261 262 263 271 272
> > 273 281 282 283 291 292 293 301 302 303 310 311 312 313 314 315 316
> > 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333
> > 334 341 342 343 344 345 351 352 353 354 361 362 363 364 371 372 373
> > 374 381 382 383 384 391 392 393 394 401 402 403 404 410 411 412 413
> > 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430
> > 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 451 452
> > 453 454 455 456 461 462 463 464 465 471 472 473 474 475 481 482 483
> > 484 485 491 492 493 494 495 501 502 503 504 505 510 511 512 513 514
> > 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
> > 549 550 551 552 553 554 555 556 561 562 563 564 565 566 567 571 572
> > 573 574 575 576 581 582 583 584 585 586 591 592 593 594 595 596 601
> > 602 603 604 605 606 610 611 612 613 614 615 616 617 618 619 620 621
> > 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
> > 656 657 658 659 660 661 662 663 664 665 666 667 671 672 673 674 675
> > 676 677 678 681 682 683 684 685 686 687 691 692 693 694 695 696 697
> > 701 702 703 704 705 706 707 710 711 712 713 714 715 716 717 718 719
> > 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
> > 771 772 773 774 775 776 777 778 781 782 783 784 785 786 787 788 789
> > 791 792 793 794 795 796 797 798 801 802 803 804 805 806 807 808 810
> > 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
> > 879 880 881 882 883 884 885 886 887 888 889 891 892 893 894 895 896
> > 897 898 899 901 902 903 904 905 906 907 908 909 910 911 912 913 914
> > 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
> >
> > On 7/23/07, Warut Roonguthai <warut822 at gmail.com> wrote:
> > > FYI, here's my Ubasic program for generating the early bird sequence:
> > >
> > > 10   X=""
> > > 20   for N=1 to 396
> > > 30   A=cutspc(str(N))
> > > 40   if instr(X,A)>0 then print N;
> > > 50   X+=A
> > > 60   next N
> > >
> > > Warut
> > >
> >
>