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 1-4 of 4 results.

A287419 Positions of 0 in A287418.

Original entry on oeis.org

1, 6, 8, 12, 14, 16, 21, 22, 26, 30, 32, 34, 39, 40, 44, 46, 51, 53, 57, 59, 61, 64, 69, 71, 75, 76, 80, 84, 86, 88, 93, 94, 98, 100, 105, 107, 111, 113, 115, 118, 123, 125, 129, 130, 134, 136, 141, 143, 147, 149, 151, 156, 157, 161, 165, 167, 169, 174, 175
Offset: 1

Views

Author

Clark Kimberling, May 25 2017

Keywords

Comments

a(n) - a(n-1) is in {1,2,3,4,5} for n >= 1; also, 3n - a(n) is in {0, 1, 2} for n >= 1. The first 20 numbers 3n - a(n) are 2, 0, 1, 0, 1, 2, 0, 2, 1, 0, 1, 2, 0, 2, 1, 2, 0, 1, 0, 1, with 0 in positions given by A287420.

Links

Crossrefs

Cf. A287418, A287420, A287421.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 2, 0}, 2->{1, 0, 2}}] &, {0}, 9]; (*A287418*)
Flatten[Position[s, 0]]; (*A287419*)
Flatten[Position[s, 1]]; (*A287420*)
Flatten[Position[s, 2]]; (*A287421*)
Position[SubstitutionSystem[{0->{0,1,2},1->{1,2,0},2->{1,0,2}},{0},{5}][[1]],0]// Flatten (* Harvey P. Dale, Jun 21 2022 *)

A287420 Positions of 1 in A287418.

Original entry on oeis.org

2, 4, 7, 10, 13, 17, 19, 23, 25, 28, 31, 35, 37, 41, 43, 47, 49, 52, 55, 58, 62, 65, 67, 70, 73, 77, 79, 82, 85, 89, 91, 95, 97, 101, 103, 106, 109, 112, 116, 119, 121, 124, 127, 131, 133, 137, 139, 142, 145, 148, 152, 154, 158, 160, 163, 166, 170, 172, 176
Offset: 1

Views

Author

Clark Kimberling, May 26 2017

Keywords

Comments

a(n) - a(n-1) is in {2,3,4} for n >= 1; also, 3n - a(n) is in {1, 2} for n >= 1. The first 20 numbers 3n - a(n) are 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, with 1 in positions given by A287419.

Links

Crossrefs

Cf. A287418, A287419, A287421.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 2, 0}, 2->{1, 0, 2}}] &, {0}, 9]; (*A287418*)
Flatten[Position[s, 0]]; (*A287419*)
Flatten[Position[s, 1]]; (*A287420*)
Flatten[Position[s, 2]]; (*A287421*)

A287421 Positions of 2 in A287418.

Original entry on oeis.org

3, 5, 9, 11, 15, 18, 20, 24, 27, 29, 33, 36, 38, 42, 45, 48, 50, 54, 56, 60, 63, 66, 68, 72, 74, 78, 81, 83, 87, 90, 92, 96, 99, 102, 104, 108, 110, 114, 117, 120, 122, 126, 128, 132, 135, 138, 140, 144, 146, 150, 153, 155, 159, 162, 164, 168, 171, 173, 177
Offset: 1

Views

Author

Clark Kimberling, May 26 2017

Keywords

Comments

a(n) - a(n-1) is in {2,3,4} for n >= 1; also, 3n - a(n) is in {0, 1} for n >= 1. The first 20 numbers 3n - a(n) are 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, with 1 in positions given by A287420.

Links

Crossrefs

Cf. A287418, A287419, A287421.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 2, 0}, 2->{1, 0, 2}}] &, {0}, 9]; (*A287418*)
Flatten[Position[s, 0]]; (*A287419*)
Flatten[Position[s, 1]]; (*A287420*)
Flatten[Position[s, 2]]; (*A287421*)

A287385 Start with 0 and repeatedly substitute 0->012, 1->210, 2->021.

Original entry on oeis.org

0, 1, 2, 2, 1, 0, 0, 2, 1, 0, 2, 1, 2, 1, 0, 0, 1, 2, 0, 1, 2, 0, 2, 1, 2, 1, 0, 0, 1, 2, 0, 2, 1, 2, 1, 0, 0, 2, 1, 2, 1, 0, 0, 1, 2, 0, 1, 2, 2, 1, 0, 0, 2, 1, 0, 1, 2, 2, 1, 0, 0, 2, 1, 0, 1, 2, 0, 2, 1, 2, 1, 0, 0, 2, 1, 2, 1, 0, 0, 1, 2, 0, 1, 2, 2, 1
Offset: 1

Views

Author

Clark Kimberling, May 25 2017

Keywords

Comments

This is the fixed point of the morphism 0->012, 1->210, 2->021 starting with 0. Let u be the (nonperiodic) sequence of positions of 0, and likewise, v for 1 and w for 2; then u(n)/n -> 3, v(n)/n -> 3, w(n)/n -> 3.
In the following guide to related sequences, column 1 indexes fixed points on {1,2,3}, and columns 2,3,4 match the position sequences of 0, 1, 2. Those sequences therefore comprise a 3-way splitting of the positive integers.
Fixed point and morphism Position sequences
A287385: 0->012, 1->210, 2->021 A287386 A287387 A287388
A287397: 0->012, 1->210, 2->102 A287398 A287399 A287400
A287401: 0->012, 1->210, 2->120 A189728 A287403 A287404
A287407: 0->012, 1->210, 2->201 A287408 A287409 A287410
A287411: 0->012, 1->120, 2->021 A287412 A287413 A287414
A287418: 0->012, 1->120, 2->102 A287419 A287420 A287421
A053838: 0->012, 1->120, 2->201 A287435 A287436 A287437
A287438: 0->012, 1->120, 2->210 A189728 A189670 A287441
A287443: 0->012, 1->201, 2->021 A287444 A287445 A287446
A287447: 0->012, 1->201, 2->102 A189724 A287449 A287450
A287451: 0->012, 1->201, 2->120 A287452 A287453 A287454
A287455: 0->012, 1->201, 2->210 A287456 A189666 A287458
A287516: 0->012, 1->102, 2->021 A287517 A287518 A189630
A287520: 0->012, 1->102, 2->120 A287521 A287522 A189630
A287524: 0->012, 1->102, 2->201 A189724 A287526 A287527
A287528: 0->012, 1->102, 2->210 A287529 A189670 A189634

Examples

			First three iterations of the morphism:  012, 012210021, 012210021021210012012021210.

Links

Crossrefs

Cf. A287386, A287387, A287388.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 1, 0}, 2->{0, 2, 1}}] &, {0}, 9]; (*A287385*)
Flatten[Position[s, 0]]; (*A287386*)
Flatten[Position[s, 1]]; (*A287387*)
Flatten[Position[s, 2]]; (*A287388*)

Extensions

Two entries in overview corrected by Georg Fischer, Sep 20 2021
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.