Talk:Summarize and say sequence: Difference between revisions
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: 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) |
: 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) |
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:: 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) |
:: 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) |
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::: Erm. Obvious as soon as you pointed it out. Sigh. --[[User:Thundergnat|Thundergnat]] 10:52, 22 August 2011 (UTC) |
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:Okay. Is the difference that in the first sequence you say what you see whilst travelling left-to-right through the digits, whilst in the second you are summarizing how many of each digit there are from highest digit to lowest? (Maybe any description could aid comprehension by also describing the derivation of that member of the sequence where they start to differ)? --[[User:Paddy3118|Paddy3118]] 07:38, 22 August 2011 (UTC) |
:Okay. Is the difference that in the first sequence you say what you see whilst travelling left-to-right through the digits, whilst in the second you are summarizing how many of each digit there are from highest digit to lowest? (Maybe any description could aid comprehension by also describing the derivation of that member of the sequence where they start to differ)? --[[User:Paddy3118|Paddy3118]] 07:38, 22 August 2011 (UTC) |
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:: 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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Revision as of 10:52, 22 August 2011
Explanation request
For the first sequence. I thought it was the second sequence until they diverge and I then new I was following the wrong method of generation. --Paddy3118 21:34, 21 August 2011 (UTC)
- 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 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. --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. --Ledrug 03:35, 22 August 2011 (UTC)
- Erm. Obvious as soon as you pointed it out. Sigh. --Thundergnat 10:52, 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. --Ledrug 03:35, 22 August 2011 (UTC)
- Okay. Is the difference that in the first sequence you say what you see whilst travelling left-to-right through the digits, whilst in the second you are summarizing how many of each digit there are from highest digit to lowest? (Maybe any description could aid comprehension by also describing the derivation of that member of the sequence where they start to differ)? --Paddy3118 07:38, 22 August 2011 (UTC)
- 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.--Thundergnat 10:52, 22 August 2011 (UTC)