A225330 A continuous "look-and-repeat" sequence (method 1).

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, 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, 2, 3, 3, 3, 1, 1, 1, 4

Offset: 1

Author

Jean-Christophe Hervé, May 12 2013

Keywords

• nonn
• easy

Comments

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.

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.

a(n) is always equal to 1, 2, 3, 4 or 5.

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.

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).

Applying the look-and-repeat principle to the sequence itself, it is simply shift four ranks to the left.

Examples

			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.
		

Crossrefs

Cf. A225331 (a close variant), A225329 (look-and-repeat by block), A005150 (original look-and-say), A225224, A221646, A225212 (continuous look-and-say versions).