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.

Previous Showing 11-18 of 18 results.

A287451 Start with 0 and repeatedly substitute 0->012, 1->201, 2->120.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 30 2017

Keywords

Comments

This is the fixed point of the morphism 0->012, 1->201, 2->120 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.
See A287385 for a guide to related sequences.

Examples

			First three iterations of the morphism:  012, 012201120, 012201120120012201201120012.

Links

Crossrefs

Cf. A287385, A287452, A287453, A287454.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 0, 1}, 2->{1, 2, 0}}] &, {0}, 9]; (*A287451*)
Flatten[Position[s, 0]]; (*A287452*)
Flatten[Position[s, 1]]; (*A287453*)
Flatten[Position[s, 2]]; (*A287454*)
SubstitutionSystem[{0->{0,1,2},1->{2,0,1},2->{1,2,0}},{0},{5}][[1]] (* Harvey P. Dale, Nov 27 2024 *)

A287447 Start with 0 and repeatedly substitute 0->012, 1->201, 2->102.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 26 2017

Keywords

Comments

This is the fixed point of the morphism 0->012, 1->201, 2->102 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.
See A287385 for a guide to related sequences.

Examples

			First three iterations of the morphism:  012, 012201102, 012201102102012201201012102.

Links

Crossrefs

Cf. A189224, A287385, A287449, A287450.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 0, 1}, 2->{1, 0, 2}}] &, {0}, 9]; (*A287447*)
Flatten[Position[s, 0]]; (*A189224*)
Flatten[Position[s, 1]]; (*A287449*)
Flatten[Position[s, 2]]; (*A287450*)

A287455 Start with 0 and repeatedly substitute 0->012, 1->201, 2->210.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 30 2017

Keywords

Comments

This is the fixed point of the morphism 0->012, 1->201, 2->210 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.
See A287385 for a guide to related sequences.

Examples

			First three iterations of the morphism:  012, 012201210, 012201210210012201210201012.

Links

Crossrefs

Cf. A287385, A287456, A287457, A287458.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{2, 0, 1}, 2->{2, 1, 0}}] &, {0}, 9]; (*A287455*)
Flatten[Position[s, 0]]; (*A287456*)
Flatten[Position[s, 1]]; (*A287457*)
Flatten[Position[s, 2]]; (*A287458*)

A287516 Start with 0 and repeatedly substitute 0->012, 1->102, 2->021.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 30 2017

Keywords

Comments

This is the fixed point of the morphism 0->012, 1->102, 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.
See A287385 for a guide to related sequences.

Examples

			First three iterations of the morphism:  012, 012102021, 012102021102012021012021102.

Links

Crossrefs

Cf. A287385, A287517, A287518, A287519.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 0, 2}, 2->{0, 2, 1}}] &, {0}, 9]; (*A287516*)
Flatten[Position[s, 0]]; (*A287517*)
Flatten[Position[s, 1]]; (*A287518*)
Flatten[Position[s, 2]]; (*A287519*)
SubstitutionSystem[{0->{0,1,2},1->{1,0,2},2->{0,2,1}},{0},{5}][[1]] (* Harvey P. Dale, Dec 22 2024 *)

A287520 Start with 0 and repeatedly substitute 0->012, 1->102, 2->120.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 30 2017

Keywords

Comments

This is the fixed point of the morphism 0->012, 1->102, 2->120 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.
It is in fact easy to see that |u(n)-3n|<3, |v(n)-3n|<3, and |w(n)-3n|<3. - Michel Dekking, Oct 02 2019
See A287385 for a guide to related sequences.

Examples

			First three iterations of the morphism:  012, 012102120, 012102120102012120102120012.

Links

Crossrefs

Cf. A287385, A287521, A287522, A189630.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 0, 2}, 2->{1, 2, 0}}] &, {0}, 9]; (*A287520*)
Flatten[Position[s, 0]]; (* A287521 *)
Flatten[Position[s, 1]]; (* A287522 *)
Flatten[Position[s, 2]]; (* A189630, conjectured *)

A287438 Start with 0 and repeatedly substitute 0->012, 1->120, 2->210.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 26 2017

Keywords

Comments

This is the fixed point of the morphism 0->012, 1->120, 2->201 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.
See A287385 for a guide to related sequences.

Examples

			First three iterations of the morphism:  012, 012120210, 012120210120210012210120012.

Links

Crossrefs

Cf. A189728, A189670, A287385, A287441.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 2, 0}, 2->{2, 1, 0}}] &, {0}, 9]; (*A287438*)
Flatten[Position[s, 0]]; (*A189728*)
Flatten[Position[s, 1]]; (*A189670*)
Flatten[Position[s, 2]]; (*A287441*)
SubstitutionSystem[{0->{0,1,2},1->{1,2,0},2->{2,1,0}},0,{5}][[1]] (* Harvey P. Dale, Nov 11 2024 *)

A287524 Start with 0 and repeatedly substitute 0->012, 1->102, 2->201.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 30 2017

Keywords

Comments

This is the fixed point of the morphism 0->012, 1->102, 2->201 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.
See A287385 for a guide to related sequences.

Examples

			First three iterations of the morphism:  012, 012102201, 012102201102012201201012102.

Links

Crossrefs

Cf. A189724, A287385, A287526, A189634.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 0, 2}, 2->{2, 0, 1}}] &, {0}, 9]; (*A287524*)
Flatten[Position[s, 0]]; (*A189724*)
Flatten[Position[s, 1]]; (*A287526*)
Flatten[Position[s, 2]]; (*A189634*)

A287528 Start with 0 and repeatedly substitute 0->012, 1->102, 2->210.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 30 2017

Keywords

Comments

This is the fixed point of the morphism 0->012, 1->102, 2->201 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.
See A287385 for a guide to related sequences.

Examples

			First three iterations of the morphism:  012, 012102210, 012102210102012210210102012.

Links

Crossrefs

Cf. A189670, A287528, A287529, A189634.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0->{0, 1, 2}, 1->{1, 0, 2}, 2->{2, 1, 0}}] &, {0}, 9]; (*A287528*)
Flatten[Position[s, 0]]; (*A287529*)
Flatten[Position[s, 1]]; (*A189670*)
Flatten[Position[s, 2]]; (*A189634*)
Previous Showing 11-18 of 18 results.

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