Talk:Look-and-say sequence

Untitled

Audioactive decay now redirects here - could someone add a mention of it? FreplySpang (talk) 19:11, 12 Apr 2005 (UTC)

Basic Properties

Having stumbled upon this page, I wanted to point out two issues I see with the basic properties section.

• The first point is untrue on the basis that at least the look-and-say sequences for a seed of 42 and 196 loop, and so do not grow indefinitely. 42 begins to loop at its 8th iteration (31123314, which generates 31123314), and 196 loops in a 5-iteration loop beginning at its 11th iteration (6122261415261719).
• The second point says "a is true unless it is not true". This is, of course, true though it doesn't seem to merit a bullet point.

Should these be deemed necessary to the article, feel free to put them back, but in the meantime I have updated the first bullet point, and removed the second. This edit can be found in the page history under (see talk page for rationale: factual correction and redundancy fix). Cheers,

    66.71.54.190 (talk) 10:48, 20 February 2008 (UTC)

I am sorry, but I have undone your edit. Your first point is a simple misunderstanding: e.g. 31123314 actually becomes 132112231114, the result of transforming a group of equal digits has the number of digits first.

The second point is more subtle. The statement is not trivial, as the sequence is a sequence of numbers, each of which can have many digits, and it speaks about what new digits can appear in numbers as the sequence develops. The digits 1, 2 and 3 can (and unless starting with 22, all eventually must) appear as the number of digits of a group at the previous stage, e.g. 3 -> 13, 33 -> 23, 12 -> 1112 -> 3112. Digits higher than 3 eventually cannot, because it is impossible to get a group of length larger than 3 unless you start out with an even longer one. --Ørjan (talk) 07:17, 21 February 2008 (UTC)

I can't believe I completely goofed on that edit. Thank you for clarifying both points.

66.71.54.190 (talk) 16:31, 21 February 2008 (UTC)

I have added the qualifier 'eventually' to the statement "In fact, any variant defined by starting with a different (seed) number will also grow indefinitely", since it is clearly possible to find a seed which causes the sequence to initially decrease. 55555 -> 55 -> 25... is an example, 333111 -> 3331 -> 3311 -> 2321... is another. I'm not sure if there are any seeds where the sequence decreases for the first five terms or more. 99.234.1.72 (talk) 21:03, 16 July 2008 (UTC)

As long as we are working in a finite base such as decimal, it can decrease for an arbitrary number of steps. 55555 can come from a sequence of 5555 digits 5, and so on without limit. This ties in with the section "Sequence or sequence of sequences?" below. If you treat it as a sequence of sequences instead then it must stop shrinking pretty quickly, since you cannot get more than three identical "digits" (actually integers) in a row, even after one step. Not sure if four terms is the limit but it cannot be much more. --Ørjan (talk) 04:38, 17 July 2008 (UTC)

Origins

The original article was in the magazine Eureka. Not only do I remember its publication, it's also listed as an earlier publication in Conway's own bibliography [1].

More on the Origins

To be more precise, Conway's original article was on pages 5-16 of Eureka 46 (January 1986). Page 4 of the same issue tells a bit more of its history (and my own part in it), going back to the Dutch team in the 1977 International Mathematical Olympiad, via the British team (including myself), via Miranda Mowbray and Eddy Welbourne (who edited Eureka 46) to Prof. Conway hearing about the problem shortly before Christmas 1983 and writing the article for Eureka 46 in January 1986. [Richard Pennington] 82.15.183.136 (talk) 20:59, 19 April 2020 (UTC)

Sequence or sequence of sequences?

The article claims the sequence is a "sequence of integers". Is this really the case? (That is, does the rule yield 1111111111 → 101 → 111011 in base 10?) Or is it a sequence of sequences of integers? (That is, does the rule yield 1111111111 → {10}1 → 1{10}11?) Gdr 20:05, 2005 Apr 12 (UTC)

Yes, it is a sequence of integers, not a sequence of sequences of integers. The rule to change one element of the sequence to the next decomposes the first integer into a string of base 10 digits, applies a transformation on them, and then converts the result into another integer. Your example does not cause a problem, because it can be proven that there will never appear a string of 10 identical digits (unless we begin with one as the first element). In fact there will never appear a string of more than 3 identical digits, because of the optimality of the transformation (11 → 21, not 1111). Redquark 21:11, 13 Apr 2005 (UTC)

Expansion request

• Does this sequence have any practical applications?
• What is the connection with run-length encoding? Is look-and-say used as part of a compression technique?
• It's a bit confused whether there is one such sequence, or if there are an infinite number because different start sequences may be used.

I see your point. In fact, Look-and-say is not a sequence. Rather, it is a rule for generating sequences from a seed value. To me, the distinction is clear. But if you worry this could be confusing to some people, why not have a go at reworking the text? Cheers

--Philopedia 23:04, 29 September 2007 (UTC)

-- Beland 21:22, 16 July 2006 (UTC)

Essentially, yes. Ignoring that base 256, rather than base 10, is used for run length encoding, it essentially _is_ look-and-say.

Suppose you have a picture that looks like this

11111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111
11111111111111111222222222211111111111111111
11111111111111122222222222222111111111111111
11111111111111222222333322222211111111111111
11111111111111222223333332222211111111111111
11111111111111222223333332222211111111111111
11111111111111222222333322222211111111111111
11111111111111122222222222222111111111111111
11111111111111111222222222211111111111111111
11111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111

"look and say" (if we limit to sequences of 9 since we have no space in base 10 for more) would result in the encoding

91919191919191919191919191919191919191919191
91919191319212919191519252919191216243629191
91115263529191911152635291919111624362919191
21925291919151921291919191919191919191919191
91919191919191919191919191919191919121

which is clearly dramatically shorter. --Random832 (contribs) 19:28, 16 April 2008 (UTC)

useless info ?

The "Basic property" : "The 70th member of the sequence has 179,691,598 digits." seems completely useless, can someone give me a reason why it should stay ? (If not, I'll remove it in a few days) --Garo 21:54, 19 March 2007 (UTC)

Undefined terms

The "Properties" section contains a lot of undefined terms that the reader is assumed to be able to deduce the meaning of:

• variant
• degenerate sequence
• seed number
• transuranic
• cosmological theorem (wikified, but no such article exists)
• generation

Some are more obvious than others, but it would help if they were all defined before use.

Further, and importantly, are these terms in actual use, or have they been coined so that they can be used in the article? If the latter is true, they should be replaced with their definitions. — Paul G 10:36, 26 October 2007 (UTC)

As far as I can see, variant has its usual English meaning, degenerate has a link, and I just added (seed) to clarify that it is the starting number in a variant sequence. Maybe iteration would be better than generation there? In any case I think those are obvious but as someone who has done work on slightly similar subjects I may be biased. I believe I was the one who added "transuranic" and someone else added "cosmological theorem", as far as I know both are terms Conway uses, as part of his work on this sequence and its variants. Actually I think the cosmological theorem is essentially the content of the item mentioning it, so I've clarified that and removed the link (I doubt it will get its own article as it only exists within the context of the L&S sequence). --Ørjan 18:39, 26 October 2007 (UTC)

Conway's polynomial

For fun, I made this: http://bendwavy.org/wp/wp-content/uploads/2010/05/conway.png The roots (crosses in the article's picture) are the points where all four colors meet. Green means the real part of Conway's polynomial is positive, and red means the imaginary part is positive. —Tamfang (talk) 02:02, 29 May 2010 (UTC)

Oops, my picture appears to put positive reals on the left. Wonder why. —Tamfang (talk) 17:18, 20 June 2017 (UTC)

Pea pattern?

Pea pattern? Stop making things up... --24.90.209.169 (talk) 02:12, 8 October 2012 (UTC)

Computer program section

The Computer program section was growing too large, clearly MOS:CODE doesn't support including more than one code example at most. I was pondering whether to keep the Python or not, but even that didn't seem particularly illustrative, so I asked someone and they said the section wasn't needed at all since it wasn't an article about an algorithm. So I just deleted it entirely. --Ørjan (talk) 10:30, 3 March 2014 (UTC)

Sounds reasonable to me. --JBL (talk) 14:21, 3 March 2014 (UTC)

Graph

I don't think the graph purporting to show the growth in the number of digits can be quite right. The blue plot looks as though it starts 1,1,1, whereas it should start 1,2,2

Kestrelsummer (talk) 22:26, 18 May 2017 (UTC)

Comparing the other colored lines, I would say the graph starts 2, 2, 2. Otherwise looks fine. Good eye. --JBL (talk) 23:43, 18 May 2017 (UTC)

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A question

Is '22' (which can be read as 'two 2s') considered some kind of Pseudo 'Look-and-say' number? ThrowawayEpic1000 (talk) 20:10, 27 September 2021 (UTC)

See the section Look-and-say sequence#Growth where this is mentioned briefly. --JBL (talk) 20:18, 27 September 2021 (UTC)