A078978 - OEIS

%I #19 Aug 31 2023 10:52:12

%S 1,2,3,4,1,2,3,1,1,2,3,4,1,2,3,2,1,2,3,4,1,2,3,1,1,2,3,4,1,2,3,3,1,2,

%T 3,4,1,2,3,1,1,2,3,4,1,2,3,2,1,2,3,4,1,2,3,1,1,2,3,4,1,2,3,4,1,2,3,4,

%U 1,2,3,1,1,2,3,4,1,2,3,2,1,2,3,4,1,2,3,1,1,2,3,4,1,2,3,3,1,2,3,4,1,2,3,1,1

%N Sequence is S(oo), where S(1)={1,2,3,4}, S(n+1)=S(n)S'(n) and S'(n) is obtained from S(n) by changing its last term using the cyclic permutation 1->2->3->4->1.

%H Paolo Xausa, <a href="/A078978/b078978.txt">Table of n, a(n) for n = 1..16384</a>

%F Limit_{n->oo} (Sum_{i=1..n} a(i))/n = 133/60; density of 1's is 19/60; density of 2's is 17/60; density of 3's is 4/15; density of 4's is 2/15.

%e Concatenate 1,2,3,4 gives 1,2,3,4,1,2,3,4 change 4 -> 1, hence first 8 terms are 1,2,3,4,1,2,3,1. Concatenate again: 1,2,3,4,1,2,3,1,1,2,3,4,1,2,3,1 change 1->2, hence first 16 terms are 1,2,3,4,1,2,3,1,1,2,3,4,1,2,3,2.

%t A078978list[i_]:=Nest[Join[#,Most[#],{Mod[Last[#],4]+1}]&,Range[4],i];

%t A078978list[5] (* Each iteration doubles the number of terms *) (* _Paolo Xausa_, Aug 31 2023 *)

%Y Cf. A010060, A078711.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Dec 19 2002