A214644 Indices of c in the sequence closed under a -> abc, b -> ab, c -> b . Start with a.

3, 9, 16, 22, 27, 32, 38, 45, 51, 56, 62, 67, 73, 80, 86, 91, 96, 102, 109, 115, 120, 126, 133, 139, 144, 150, 157, 163, 168, 173, 179, 186, 192, 197, 203, 208, 214, 221, 227, 232, 237, 243, 250, 256, 261, 267, 274, 280, 285, 290, 296, 303, 309, 314, 320, 327

Offset

1,1

Comments

Indices of 3 in A214640.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Example

Start: a
Rules:
  a --> abc
  b --> ab
  c --> b
-------------
0:   (#=1)
  a
1:   (#=3)
  abc
2:   (#=6)
  abcabb
3:   (#=13)
  abcabbabcabab
4:   (#=29)
  abcabbabcabababcabbabcababcab
5:   (#=64)
  abcabbabcabababcabbabcababcababcabbabcabababcabbabcababcabbabcab
    3    9       16    22   27 ... (positions of 'c')

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) option remember; local i, k; i:=1;
      for k from 1+`if`(n=1, 0, a(n-1)) do
        while nops(S(i))<k do i:=i+1 od;
        if S(i)[k] = 3 then return k fi
      od
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 28 2012

Mathematica

SubstitutionSystem[{"a" -> {"a", "b", "c"}, "b" -> {"a", "b"}, "c" -> {"b"}}, {"a"}, 8] // Last // Position[#, "c"]& // Flatten (* Jean-François Alcover, Nov 04 2020 *)

Crossrefs

Cf. A214640, A214641, A214642.

Sequence in context: A299636 A271491 A359618 * A184529 A338020 A020967

Adjacent sequences: A214641 A214642 A214643 * A214645 A214646 A214647

Keyword

nonn,easy

Author

Philippe Deléham, Jul 24 2012

Status

approved