|
%I #24 Jan 19 2019 04:15:43
%S 1,1,1,1,4,4,1,2,2,4,1,1,1,2,2,2,1,1,4,3,3,1,3,3,2,2,2,1,1,1,4,2,2,3,
%T 1,1,1,2,2,3,3,3,2,3,3,1,1,1,4,2,2,2,1,1,3,3,3,1,2,2,2,3,3,3,1,1,2,2,
%U 2,3,3,3,1,1,1,4
%N A continuous "look-and-repeat" sequence (method 1).
%C A variant of the 'look-and-repeat' sequence A225329, without run cut-off. It describes at each step the preceding digits by repeating the frequency number.
%C The sequence is determined by triples of digits. The first two terms of a triple are the repeated frequency and the last term is the digit.
%C a(n) is always equal to 1, 2, 3, 4 or 5.
%C However, the occurrence of 4 is specific to this variant (method and seed), and only due to the initial sequence of four 1's. No other series of four identical digit happens in the sequence.
%C There are different optional rules to build such a sequence. This method 1 does not consider already said digits, unless if the length of the sequence of repeated figures to which they belongs change : this happens only once at the beginning, with the first 1 which is considered twice (and this brings up the 4): 1 -> 1,1,1 -> 4,4,1. The variant A225330 never considers already said digit (and does not contain 4). With other seeds (for example, 2 or 3), this special case at the beginning does not arise, and both variants coincide (and do not contain 4).
%C Applying the look-and-repeat principle to the sequence itself, it is simply shift four ranks to the left.
%e a(1) = 1, you then see "one 1" and repeating "one", a(2) = a(3) = 1 (one) and a(4) = 1; Looking at a(1), a(2), a(3), and a(4) altogether, you then see "four 1": a(5) = a(6) = 4 and a(7) = 1, etc.
%Y Cf. A225331 (a close variant), A225329 (look-and-repeat by block), A005150 (original look-and-say), A225224, A221646, A225212 (continuous look-and-say versions).
%K nonn,easy
%O 1,5
%A _Jean-Christophe Hervé_, May 12 2013
|
