A225329 Look-and-repeat: similar to look-and-say except frequency is repeated.

1, 111, 331, 223111, 222113331, 332221333111, 223332111333331, 222333112331553111, 332333221112223111225113331, 223112333222331332113331222115221333111

Offset: 1

Author

Jean-Christophe Hervé, May 12 2013

Keywords

• nonn
• base

Comments

Repeated frequency followed by digit-indication. Repeating the frequency allows 5 to appear, in addition to 1, 2 and 3 which are already contained in Conway's original look-and-say sequence. However, 4 still does not appear.

The sequence is determined by triples of digits. The first two terms of a triple are the repeated figure and the last term is the digit.

Therefore, sequences of form xy (x != y), xxyy can never appear. A fortiori, the sequence never contains series of four identical digits, but contains series of five 3, which make appear the 5's (55 and 5). However five 5's never appear. Proof: suppose it appears for the first time in a(n)-a(n+4); because of 'five five 5' in 55555, it would imply that 55555 appears form a smaller n, which is a contradiction. By the same argument, 555 also never appear.

Also 22222 or 11111 are impossible : 22222 would imply a preceding 22yy and 11111 a preceding 1x (x != 1), but both cannot exist.

All terms end with 1 (the seed) and, except the first two, begin with 2 or 3.

Examples

			The term after 331 is obtained by saying (repeating) two two 3, one one 1, which gives 223111.
		

Crossrefs

Cf. A005150 (original look-and-say), A225224, A221646, A225212 (continuous look-and-say versions), A225330, A225331 (continuous look-and-repeat).