A078978 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.

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, 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, 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

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..16384

Formula

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.

Example

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.

Mathematica

A078978list[i_]:=Nest[Join[#, Most[#], {Mod[Last[#], 4]+1}]&, Range[4], i];
A078978list[5] (* Each iteration doubles the number of terms *) (* Paolo Xausa, Aug 31 2023 *)

Crossrefs

Cf. A010060, A078711.

Sequence in context: A073057 A084310 A214063 * A322424 A309198 A256914

Adjacent sequences: A078975 A078976 A078977 * A078979 A078980 A078981

Keyword

nonn

Author

Benoit Cloitre, Dec 19 2002

Status

approved