cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 10 results.

A070788 Positive integers n such that the Reverse and Add! trajectory of n (presumably) does not join the trajectory of any m < n.

Original entry on oeis.org

1, 3, 5, 7, 9, 100, 102, 106, 108, 111, 112, 113, 114, 116, 117, 118, 119, 122, 124, 128, 133, 135, 137, 138, 166, 184, 186, 196, 199, 359, 399, 459, 539, 659, 679, 739, 759, 779, 799, 859, 879, 919, 939, 959, 979, 999, 1000, 1006, 1011, 1013, 1022, 1033, 1037
Offset: 1

Views

Author

Klaus Brockhaus, May 07 2002, revised Oct 15 2003

Keywords

Comments

The conjecture that the trajectories of the terms of this sequence do not join is based on the observation that if the trajectories of two integers below 10000 join, this happens after at most 15 steps, while for any two terms the trajectories do not join within 1200 steps. For pairs from 1, 3, 5, 7, 9, 100, 102, 106 this has even been checked for 10000 steps.
The positive integers are the domain of the equivalence relation 'the trajectories of a and b join'; each of its presumably infinitely many equivalence classes is represented by a term of this sequence. Each class contains infinitely many integers (cf. A070789 - A070798). In such a class the relation 'the trajectory of a is part of the trajectory of b' is a partial order for which a term c is a maximal element if it is in A067031 (integers not of the form k + reverse(k) for any k) and the integer at which the trajectories of a and b join is the greatest lower bound of a and b.

Examples

			The trajectory of 2 is part of the trajectory of 1; the trajectory of 3 does not join the trajectory of 1 within 10000 steps; the trajectory of 5 does not join the trajectory of 1 or of 3 within 10000 steps.

Links

Crossrefs

Cf. A006960, A063048, A067031, A070789 - A070798, A063049.

Programs

  • Mathematica
    limit = 10^3; utraj = {};
Select[Range[1037], (x = NestList[ # + IntegerReverse[#] &, #, limit]; If[Intersection[x, utraj] == {}, utraj = Union[utraj, x]; True, utraj = Union[utraj, x]]) &] (* Robert Price, Oct 20 2019 *)

A070791 Integers n such that the 'Reverse and Add!' trajectory of n joins the trajectory of 5.

Original entry on oeis.org

5, 10, 11, 13, 17, 20, 22, 26, 31, 35, 40, 44, 53, 62, 71, 79, 80, 88, 97, 115, 142, 158, 170, 176, 185, 214, 241, 257, 275, 284, 313, 329, 340, 356, 374, 383, 412, 428, 455, 469, 473, 482, 511, 527, 554, 568, 572, 581, 599, 610, 626, 649, 653, 667, 671, 680
Offset: 1

Views

Author

Klaus Brockhaus, May 07 2002

Keywords

Examples

			The trajectory of 10 is part of the trajectory of 5; the trajectory of 340 joins the trajectory of 5 at 88088 after 7 steps.

Links

Crossrefs

Cf. A070788 - A070790, A070792 - A070798, A063049.

Programs

  • Mathematica
    limit = 10^3; x = NestList[ # + IntegerReverse[#] &, 5, limit];
Select[Range[680],
 Intersection[NestList[ # + IntegerReverse[#] &, #, limit],
x] != {} &] (* Robert Price, Oct 20 2019 *)

A070796 Integers n such that the 'Reverse and Add!' trajectory of n joins the trajectory of 106.

Original entry on oeis.org

106, 152, 179, 205, 251, 278, 304, 350, 377, 379, 403, 476, 478, 479, 502, 509, 575, 577, 578, 601, 608, 674, 676, 677, 700, 707, 773, 775, 776, 806, 872, 874, 875, 905, 971, 973, 974, 1019, 1054, 1060, 1082, 1093, 1109, 1144, 1150, 1172, 1183, 1199
Offset: 1

Views

Author

Klaus Brockhaus, May 07 2002

Keywords

Examples

			The trajectory of 707 is part of the trajectory of 106; the trajectory of 775 joins the trajectory of 106 at 48884 after 5 steps.

Links

Crossrefs

Cf. A070788 - A070795, A070797, A070798, A063049.

Programs

  • Mathematica
    limit = 10^3; x = NestList[ # + IntegerReverse[#] &, 106, limit];
Select[Range[1199],
 Intersection[NestList[ # + IntegerReverse[#] &, #, limit],
x] != {} &] (* Robert Price, Oct 20 2019 *)

A070789 Integers n such that the 'Reverse and Add!' trajectory of n joins the trajectory of 1.

Original entry on oeis.org

1, 2, 4, 8, 16, 25, 34, 43, 52, 59, 61, 68, 70, 77, 86, 95, 104, 109, 151, 154, 155, 157, 203, 208, 209, 250, 253, 254, 256, 302, 307, 308, 352, 353, 355, 401, 406, 407, 409, 451, 452, 454, 500, 505, 506, 508, 550, 551, 553, 604, 605, 607, 650, 652, 703, 704
Offset: 1

Views

Author

Klaus Brockhaus, May 07 2002

Keywords

Examples

			The trajectory of 2 is part of the trajectory of 1; the trajectory of 401 joins the trajectory of 1 at 1111 after 3 steps.

Links

Crossrefs

Cf. A070788, A070790 - A070798, A063049.

Programs

  • Mathematica
    limit = 10^3; x = NestList[ # + IntegerReverse[#] &, 1, limit];
Select[Range[704],
 Intersection[NestList[ # + IntegerReverse[#] &, #, limit],
x] != {} &] (* Robert Price, Oct 20 2019 *)

A070790 Integers n such that the 'Reverse and Add!' trajectory of n joins the trajectory of 3.

Original entry on oeis.org

3, 6, 12, 15, 21, 24, 30, 33, 39, 42, 48, 51, 57, 60, 66, 69, 75, 78, 84, 87, 93, 96, 132, 159, 165, 177, 219, 231, 258, 264, 276, 318, 330, 357, 363, 375, 417, 429, 456, 462, 474, 516, 528, 555, 561, 573, 579, 615, 627, 654, 660, 672, 678, 699, 714, 726, 753
Offset: 1

Views

Author

Klaus Brockhaus, May 07 2002

Keywords

Examples

			The trajectory of 6 is part of the trajectory of 3; the trajectory of 375 joins the trajectory of 3 at 9768 after 3 steps.

Links

Crossrefs

Cf. A070788, A070789, A070791 - A070798, A063049.

Programs

  • Mathematica
    limit = 10^3; x = NestList[ # + IntegerReverse[#] &, 3, limit];
Select[Range[753],
 Intersection[NestList[ # + IntegerReverse[#] &, #, limit],
x] != {} &] (* Robert Price, Oct 20 2019 *)

A070792 Integers n such that the 'Reverse and Add!' trajectory of n joins the trajectory of 7.

Original entry on oeis.org

7, 14, 19, 23, 28, 29, 32, 37, 38, 41, 46, 47, 49, 50, 55, 56, 58, 64, 65, 67, 73, 74, 76, 82, 83, 85, 89, 91, 92, 94, 98, 110, 121, 136, 143, 187, 220, 235, 242, 286, 334, 341, 385, 433, 440, 484, 532, 569, 583, 631, 668, 682, 719, 730, 767, 781, 818, 866, 869
Offset: 1

Views

Author

Klaus Brockhaus, May 07 2002

Keywords

Examples

			The trajectory of 14 is part of the trajectory of 7; the trajectory of 235 joins the trajectory of 7 at 8872688 after 13 steps.

Links

Crossrefs

Cf. A070788 - A070791, A070793 - A070798, A063049.

Programs

  • Mathematica
    limit = 10^3; x = NestList[ # + IntegerReverse[#] &, 7, limit];
Select[Range[869],
 Intersection[NestList[ # + IntegerReverse[#] &, #, limit],
x] != {} &] (* Robert Price, Oct 20 2019 *)

A070793 Integers n such that the 'Reverse and Add!' trajectory of n joins the trajectory of 9.

Original entry on oeis.org

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 198, 297, 396, 495, 594, 693, 792, 891, 990, 1017, 1035, 1044, 1089, 1107, 1125, 1134, 1179, 1215, 1224, 1269, 1305, 1314, 1359, 1404, 1449, 1539, 1629, 1719, 1809, 1899, 1989, 2016, 2034, 2043, 2088, 2106, 2124
Offset: 1

Views

Author

Klaus Brockhaus, May 07 2002

Keywords

Examples

			The trajectory of 18 is part of the trajectory of 9; the trajectory of 1215 joins the trajectory of 9 at 40293 after 3 steps.

Links

Crossrefs

Cf. A070788 - A070792, A070794 - A070798, A063049.

Programs

  • Mathematica
    limit = 10^3; x = NestList[ # + IntegerReverse[#] &, 9, limit];
Select[Range[2124],
 Intersection[NestList[ # + IntegerReverse[#] &, #, limit],
x] != {} &] (* Robert Price, Oct 20 2019 *)

A070794 Integers n such that the 'Reverse and Add!' trajectory of n joins the trajectory of 100.

Original entry on oeis.org

100, 101, 103, 107, 188, 193, 200, 202, 206, 287, 292, 299, 301, 305, 386, 391, 398, 400, 404, 485, 490, 497, 503, 584, 596, 602, 683, 695, 701, 709, 782, 794, 800, 808, 881, 893, 907, 980, 992, 1034, 1069, 1076, 1124, 1159, 1166, 1214, 1249, 1256, 1291
Offset: 1

Views

Author

Klaus Brockhaus, May 07 2002

Keywords

Examples

			The trajectory of 101 is part of the trajectory of 100; the trajectory of 485 joins the trajectory of 100 at 61105 after 5 steps.

Links

Crossrefs

Cf. A070788 - A070793, A070795 - A070798, A063049.

Programs

  • Mathematica
    limit = 10^3; x = NestList[ # + IntegerReverse[#] &, 100, limit];
Select[Range[1291],
 Intersection[NestList[ # + IntegerReverse[#] &, #, limit],
x] != {} &] (* Robert Price, Oct 20 2019 *)

A070795 Integers n such that the 'Reverse and Add!' trajectory of n joins the trajectory of 102.

Original entry on oeis.org

102, 105, 150, 156, 201, 204, 255, 300, 303, 309, 354, 402, 408, 453, 501, 507, 552, 600, 606, 609, 651, 705, 708, 750, 804, 807, 903, 906, 1032, 1065, 1122, 1155, 1212, 1245, 1290, 1302, 1335, 1380, 1425, 1470, 1515, 1560, 1605, 1650, 1740, 1830, 1896
Offset: 1

Views

Author

Klaus Brockhaus, May 07 2002

Keywords

Examples

			The trajectory of 303 is part of the trajectory of 102; the trajectory of 750 joins the trajectory of 102 at 6666 after 3 steps.

Links

Crossrefs

Cf. A070788 - A070794, A070796 - A070798, A063049.

Programs

  • Mathematica
    limit = 10^3; x = NestList[ # + IntegerReverse[#] &, 102, limit];
Select[Range[1896],
 Intersection[NestList[ # + IntegerReverse[#] &, #, limit],
x] != {} &] (* Robert Price, Oct 20 2019 *)

A070797 Integers n such that the 'Reverse and Add!' trajectory of n joins the trajectory of 108.

Original entry on oeis.org

108, 126, 144, 153, 162, 171, 180, 189, 207, 225, 243, 252, 261, 270, 279, 288, 306, 324, 342, 351, 360, 378, 387, 405, 423, 441, 450, 477, 486, 504, 522, 540, 549, 576, 585, 603, 621, 648, 675, 684, 702, 720, 747, 774, 783, 801, 846, 873, 882, 900, 909
Offset: 1

Views

Author

Klaus Brockhaus, May 07 2002

Keywords

Comments

It appears that the first differences of this sequence are always a multiple of 9. - Robert Price, Oct 20 2019

Examples

			The trajectory of 909 is part of the trajectory of 108; the trajectory of 126 joins the trajectory of 108 at 4069593 after 12 steps.

Links

Crossrefs

Cf. A070788 - A070796, A070798, A063049.

Programs

  • Mathematica
    limit = 10^3; x = NestList[ # + IntegerReverse[#] &, 108, limit];
Select[Range[909],
Intersection[NestList[ # + IntegerReverse[#] &, #, limit],
x] != {} &] (* Robert Price, Oct 20 2019 *)
Showing 1-10 of 10 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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