

A225212


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


12



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
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OFFSET

1,4


COMMENTS

A variant of the 'LookandSay' 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] (* JeanFrançois Alcover, May 02 2013 *)


CROSSREFS

Cf. A005150, A225224.
Sequence in context: A066975 A291634 A098877 * A091088 A249781 A115627
Adjacent sequences: A225209 A225210 A225211 * A225213 A225214 A225215


KEYWORD

nonn,easy


AUTHOR

JeanChristophe Hervé, May 01 2013


STATUS

approved



