A225212 A "Look and Say" sequence (with nested repetitions).

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

Offset

1,4

Comments

A variant of the 'Look-and-Say' sequence A005150 that describes at each step the preceding digits altogether since the beginning. The sequence is built by blocks, each new block describing the preceding ones, always returning to the beginning: 1; 1,1; 3,1; 3,1,1,3,1,1; 3,1,1,3,1,1,1,3,2,1,1,3,2,1; etc. This generates indefinitely nested repeats: 31, 311311, 311311, ... The sequence A225224 is a variant that avoids these repetitions.

The size of the block of rank k equals 2^k for k = 1 or 2, and is < 2^k for any k >= 3.

Except the first two blocks, each block begins with 31 and ends with 1.

As in the original A005150, a(n) is always equal to 1, 2 or 3. The subsequence 3,3,3 never appears.

Links

John Cerkan, Table of n, a(n) for n = 1..10000

Example

a(1) = 1, you then see "one 1": a(2) = 1 (one) and a(3) = 1; Looking at a(1), a(2) and a(3) altogether, you then see "three 1" : a(4) = 3 and a(5) = 1. The sequence is then built by blocks, each new block describing the preceding ones since the beginning of the sequence: 1; 1,1; 3,1; 3,1,1,3,1,1; etc.

Mathematica

f[seq_] := Join[seq, {Length[#], First[#]}& /@ Split[seq]] // Flatten; Nest[f, {1}, 5] (* Jean-François Alcover, May 02 2013 *)

Crossrefs

Cf. A005150, A225224.

Sequence in context: A355879 A291634 A098877 * A091088 A335915 A249781

Adjacent sequences: A225209 A225210 A225211 * A225213 A225214 A225215

Keyword

nonn,easy

Author

Jean-Christophe Hervé, May 01 2013

Status

approved