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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?

  Submitted by Bob Smith    
Rating: 3.7143 (7 votes)
Solution: (Hide)
Part 1:
1,7,6,5,4,7,3,5,7,2,7,5,3,7,4,5,6,7,1
1,8,7,6,5,4,7,3,8,5,7,2,7,5,8,3,7,4,5,6,7,8,1
For row N, insert N between any two values that sum to N

Several Perplexers identified these as denominators in a Farey sequence. If a/b, c/d, and e/f are successive terms in a Farey sequence, then c = a+e and d = b+f.

Part 2:
The length of the sequences in each row is prime

Part 3:
The prime values continue until N=9. At N=10, the length of the sequence is 33.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(4): SpoilerBob Smith2005-11-02 09:15:31
re(3): Spoilerpcbouhid2005-11-01 20:31:02
re(2): SpoilerTristan2005-11-01 19:59:43
Hints/TipsNext two linesBob Smith2005-11-01 10:45:53
re(2): Agree with pcbouhidgoFish2005-11-01 10:05:17
re: Spoilerpcbouhid2005-11-01 09:57:12
re: SpoilerBryan2005-11-01 09:09:13
SolutionSpoilerTristan2005-10-31 21:03:56
Hints/TipsAn ideaTristan2005-10-31 20:33:18
SolutionFuller solutiongoFish2005-10-31 18:46:14
SolutiongoFish2005-10-31 18:10:58
Some Thoughtscounting the number of numberstanx2005-10-31 15:26:36
my guesspcbouhid2005-10-31 14:58:31
re: This works, but is it what Bob had in mind (don't know if spoiler)Bob Smith2005-10-31 14:26:25
Some ThoughtsThis works, but is it what Bob had in mind (don't know if spoiler)Charlie2005-10-31 13:49:37
Some Thoughtsa thoughtThoughtProvoker2005-10-31 12:37:09
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