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?
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Submitted by Bob Smith
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Rating: 3.7143 (7 votes)
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Solution:
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(Hide)
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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.
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