A214640 A ternary sequence : closed under 1 -> 123, 2 -> 12, 3 -> 2 . Start with 1 .

1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 1, 2, 1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

Start: 1
Rules:
  1 --> 123
  2 --> 12
  3 --> 2
-------------
0:   (#=1)
  1
1:   (#=3)
  123
2:   (#=6)
  123122
3:   (#=13)
  1231221231212
4:   (#=29)
  12312212312121231221231212312
5:   (#=64)
  1231221231212123122123121231212312212312121231221231212312212312

Maple

S:= proc(n) option remember; `if`(n=0, [1], subs(x=[1, 2, 3][],
       y=[1, 2][], z=2, subs(1=x, 2=y, 3=z, S(n-1))))
    end:
a:= proc(n) local k;
       for k while nops(S(k))<n do od; S(k)[n]
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 28 2012

Mathematica

SubstitutionSystem[{1 -> {1, 2, 3}, 2 -> {1, 2}, 3 -> {2}}, {1}, 6] // Last (* Jean-François Alcover, Nov 04 2020 *)

Crossrefs

Cf. A214260, A214641, A214642, A214644.

Sequence in context: A289585 A128864 A106798 * A224965 A194298 A194306

Adjacent sequences: A214637 A214638 A214639 * A214641 A214642 A214643

Keyword

nonn,easy

Author

Philippe Deléham, Jul 23 2012

Status

approved