A105265 Concatenation of letters of words obtained from axiom "1" and the iterates of the substitutions '1' -> "12", '2' -> "3", '3' -> "4", '4' -> "1".

1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 1, 2, 3, 4, 1, 2, 3, 4, 1, 1, 2, 3, 4

Offset: 0

Author

Roger L. Bagula, Apr 15 2005

Keywords

• nonn
• easy
• less

Comments

Let W() be the substitution defined above. If we define the sequence S(n) by S(0) = {1}, S(n+1) = S(n) + W(S(n)), then this sequence is the limiting sequence of S(n) as n approaches infinity. - Charlie Neder, Jul 11 2018

Links

• Charlie Neder, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A073058.

Programs

Mathematica

s[1] = {1, 2}; s[2] = {3}; s[3] = {4}; s[4] = {1};
t[a_] := Join[a, Flatten[s /@ a]];
p[0] = {1}; p[1] = t[{1}]; p[n_] := t[p[n - 1]]
aa = p[6]

Extensions

New name from Joerg Arndt, Jul 14 2018