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Palindromic sequences (Posted on 2005-10-31) Difficulty: 3 of 5
1,1
1,2,1
1,3,2,3,1
1,4,3,2,3,4,1
1,5,4,3,5,2,5,3,4,5,1
1,6,5,4,3,5,2,5,3,4,5,6,1

What are the next several lines and how are they formed?

Do the sequences have any special feature?

Does the pattern continue indefinitely?

See The Solution Submitted by Bob Smith    
Rating: 3.7143 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts This works, but is it what Bob had in mind (don't know if spoiler) | Comment 2 of 16 |
(In reply to a thought by ThoughtProvoker)

Following up on ThoughtProvoker's thought, each row is to have the next prime number of elements.

The first is always 1 and the second is one higher than the second in the row before. The third is the second from the preceding row; the fourth from the third, etc., but stop before taking from the middle row. At that point start taking from the second, third, etc. elements of the new line being built (thus the second 5 on row 5 being a copy of the first). But take the middle number from the previous middle number. The remaining numbers are the reverse of the first several, in order to make a palindrome.

The resulting continuation of the left side then looks like:


                                                                   1  2
                                                                1  3  2
                                                             1  4  3  2
                                                       1  5  4  3  5  2
                                                    1  6  5  4  3  5  2
                                              1  7  6  5  4  3  5  7  2
                                           1  8  7  6  5  4  3  5  7  2
                                     1  9  8  7  6  5  4  3  5  7  9  2
                            1 10  9  8  7  6  5  4  3  5  7  9 10  9  2
                         1 11 10  9  8  7  6  5  4  3  5  7  9 10  9  2
                1 12 11 10  9  8  7  6  5  4  3  5  7  9 10  9 12 11  2
          1 13 12 11 10  9  8  7  6  5  4  3  5  7  9 10  9 12 11 13  2
       1 14 13 12 11 10  9  8  7  6  5  4  3  5  7  9 10  9 12 11 13  2
 1 15 14 13 12 11 10  9  8  7  6  5  4  3  5  7  9 10  9 12 11 13 15  2

Edited on October 31, 2005, 1:51 pm
  Posted by Charlie on 2005-10-31 13:49:37

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