Talk:Summarize and say sequence: Difference between revisions
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Thundergnat moved page Talk:Self-referential sequence to Talk:Summarize and say sequence: Better descriptive name
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==Explanation request==
For the first sequence. I thought it was the second sequence until they diverge and I then
: The first sequence is just an example, not central to the task. In that one you generate the next term by reading out loud, if you will, the digits. 0 is one zero (10), next there is (reading the term) one one, one zero (1110) then three ones, one zero (3110) See [http://oeis.org/A001155 A001155]. I just mentioned it because it is probably the most commonly cited self-referential sequence in my experience. It is just a coincidence that they are the same for the first five elements when seeded with 0. It may be worth have generation of that sequence as part of the task (or a separate task) but I thought the second sequence was more interesting. As an aside, for the second sequence, I think there may be only one sequence that takes more than 21 steps to converge. A string of 900 9s will converge in 22 steps. There may be others but I haven't, and can't practically do an exhaustive search. --[[User:Thundergnat|Thundergnat]] 00:40, 22 August 2011 (UTC)
:: There certainly will be longer sequences. Take a number with 900 digit 9s, its next step is 9009, so length is +1. That number itself ends with 9, so you can construct another number with a gadzillion digits of 9s which is again length +1, and this can go on ad infinitum. --[[User:Ledrug|Ledrug]] 03:35, 22 August 2011 (UTC)
::: Erm. Obvious as soon as you pointed it out. Sigh. --[[User:Thundergnat|Thundergnat]] 10:52, 22 August 2011 (UTC)
:Okay. Is the difference that in the first sequence you say what you see whilst
:: Perhaps an easier way to think of it is to take the term, say 13123110, sort the digits high to low: 33211110, then read it off as in the look-and-say sequence (which is what the first sequence is basically): 2 3s, 1 2, 4 1s, 1 0 or 23124110. In look-and-say, you don't sort the digits first. Here, you do.--[[User:Thundergnat|Thundergnat]] 10:52, 22 August 2011 (UTC)
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::: OEIS says "this kind of counting sequence", so maybe "digit counting sequence"? If name has to be "*verb*-and say", the verb is better as "Count" IMO since sorting is not essential. --[[User:Ledrug|Ledrug]] 00:42, 24 August 2011 (UTC)
::::+1 --[[User:Paddy3118|Paddy3118]] 04:55, 25 August 2011 (UTC)
::: For the task name, the word '''sort''' (as in sorting) isn't necessary to the task, '''counting''' is (or is implied by ''looking''). The '''REXX''' example doesn't do a sort. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 23:08, 18 August 2018 (UTC)
:Sequences which derive a value from the previous value have a nice, well-established name: they are called ''recurrences''. The particular recurrences being discussed here are based on calculations that work with the base ten representation of integers. This kind of manipulation is ''typographical'': essentially it works with the printed representation, which leads us to ''typographical recurrence''. Knuth's term ''semi-numerical'' could apply here: the calculation performs counting over the base 10 typography of the previous term, and counts then turn into typography in the next term. This suggests ''semi-numerical recurrence''.[[User:Kazinator|Kazinator]] ([[User talk:Kazinator|talk]]) 16:50, 20 July 2014 (UTC)
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