Talk:Summarize and say sequence: Difference between revisions
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Thundergnat (talk | contribs) (Some clarification) |
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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. --[[User:Paddy3118|Paddy3118]] 21:34, 21 August 2011 (UTC) |
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. --[[User:Paddy3118|Paddy3118]] 21:34, 21 August 2011 (UTC) |
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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) |
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Revision as of 03:35, 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)