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 1-3 of 3 results.

A287160 0-limiting word of the morphism 0->10, 1->21, 2->0.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 22 2017

Keywords

Comments

Starting with 0, the first 4 iterations of the morphism yield words shown here:
1st: 10
2nd: 2110
3rd: 0212110
4th: 1002010212110
The 0-limiting word is the limit of the words for which the number of iterations is congruent to 0 mod 3.
Let u be the sequence of positions of 0, and likewise, v for 1 and w for 2. Let U, V, W be the limits of u(n)/n, v(n)/n, w(n)/n, respectively. Then 1/U + 1/V + 1/W = 1, where
U = 3.079595623491438786010417...,
V = 2.324717957244746025960908...,
W = U + 1 = 4.079595623491438786010417....
If n >=2, then u(n) - u(n-1) is in {1,2,3,4,6}, v(n) - v(n-1) is in {1,2,3,4}, and w(n) - w(n-1) is in {2,3,4,5,7}.

Examples

			The 3rd and 6th iterates are 0212110 and 0212110211010021211010021100210212110.

Links

Crossrefs

Cf. A287106, A287156, A287161, A287162, A287163.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 1}, 2 -> 0}] &, {0}, 9] (* A287160 *)
Flatten[Position[s, 0]] (* A287161 *)
Flatten[Position[s, 1]] (* A287162 *)
Flatten[Position[s, 2]] (* A287163 *)

A287161 Positions of 0 in A287160.

Original entry on oeis.org

1, 7, 11, 13, 14, 20, 22, 23, 27, 28, 31, 37, 41, 43, 44, 48, 49, 52, 58, 60, 61, 64, 70, 71, 77, 81, 83, 84, 90, 92, 93, 97, 98, 101, 107, 109, 110, 113, 119, 120, 126, 130, 132, 133, 137, 138, 141, 147, 148, 154, 158, 160, 161, 164, 170, 174, 176, 177, 183
Offset: 1

Views

Author

Clark Kimberling, May 22 2017

Keywords

Links

Crossrefs

Cf. A287160, A287162, A287163.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 1}, 2 -> 0}] &, {0}, 9] (* A287160 *)
Flatten[Position[s, 0]] (* A287161 *)
Flatten[Position[s, 1]] (* A287162 *)
Flatten[Position[s, 2]] (* A287163 *)

A287162 Positions of 1 in A287160.

Original entry on oeis.org

3, 5, 6, 9, 10, 12, 16, 18, 19, 21, 25, 26, 30, 33, 35, 36, 39, 40, 42, 46, 47, 51, 54, 56, 57, 59, 63, 66, 68, 69, 73, 75, 76, 79, 80, 82, 86, 88, 89, 91, 95, 96, 100, 103, 105, 106, 108, 112, 115, 117, 118, 122, 124, 125, 128, 129, 131, 135, 136, 140, 143
Offset: 1

Views

Author

Clark Kimberling, May 22 2017

Keywords

Links

Crossrefs

Cf. A287160, A287161, A287163.

Programs

  • Mathematica
    s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {2, 1}, 2 -> 0}] &, {0}, 9] (* A287160 *)
Flatten[Position[s, 0]] (* A287161 *)
Flatten[Position[s, 1]] (* A287162 *)
Flatten[Position[s, 2]] (* A287163 *)
Showing 1-3 of 3 results.

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

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