A214641 Indices of a in the sequence closed under a -> abc, b -> ab, c -> b . Start with a.

1, 4, 7, 10, 12, 14, 17, 20, 23, 25, 28, 30, 33, 36, 39, 41, 43, 46, 49, 52, 54, 57, 60, 63, 65, 68, 71, 74, 76, 78, 81, 84, 87, 89, 92, 94, 97, 100, 103, 105, 107, 110, 113, 116, 118, 121, 124, 127, 129, 131, 134, 137, 140, 142, 145, 148, 151, 153, 155, 158

Offset

1,2

Comments

Indices of 1 in A214640.

Links

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

Example

a -> abc -> abcabb -> abcabbabcabab -> abcabbabcabababcabbabcababcab -> ...

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] = 1 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"}, 7] // Last // Position[#, "a"]& // Flatten (* Jean-François Alcover, Nov 04 2020 *)

Crossrefs

Cf. A214640, A214642, A214644.

Sequence in context: A097703 A310674 A104036 * A178598 A310675 A176292

Adjacent sequences: A214638 A214639 A214640 * A214642 A214643 A214644

Keyword

nonn

Author

Philippe Deléham, Jul 23 2012

Status

approved