A225331 A continuous "look-and-repeat" sequence (method 2).

1, 1, 1, 1, 3, 3, 1, 2, 2, 3, 1, 1, 1, 2, 2, 2, 1, 1, 3, 3, 3, 1, 3, 3, 2, 2, 2, 1, 3, 3, 3, 1, 1, 1, 2, 2, 3, 3, 3, 2, 1, 1, 1, 3, 3, 3, 3, 3, 1, 2, 2, 2, 3, 3, 3, 1, 1, 2, 3, 3, 1, 5, 5, 3, 1, 1, 1, 3, 3, 2, 3, 3

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.

There are different optional rules to build such a sequence. This method 2 never considers twice the already said digits.

With this rule and seed, a(n) is always equal to 1, 2, 3 or 5, and the sequence is the simple concatenation of the look-and-repeat sequence by block A225329. This is because all blocks of A225329 begin with 2 or 3 and end with 2 and therefore, there is no possible interaction between blocks after concatenation.

It never contains runs of exactly four identical digits (except the first four ones), but it does contain runs of five identical digits. However, five 5's never appear. Proof: suppose '55555' appears for the first time in a(n)..a(n+4); because of 'five five 5' in 55555, it would imply that 55555 appears from a smaller n, which is a contradiction.

Examples

			a(1) = 1, then a(2) = a(3) = a(4) = 1 (one one 1). Leaving out the first 1 already said, we now have three 1's, then a(5) = a(6) = 3, and a(7) = 1, etc.
		

Crossrefs

Cf. A225330 (a close variant with 4's), A225329 (look-and-repeat by block), A005150 (original look-and-say), A225224, A221646, A225212 (continuous look-and-say versions).