Difference between revisions of "Sequence of length 1112"

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(Subsequence analysis)
 
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This reflects the beginning of the subsequences. There are some emerging methods for analysing over the whole length which may give insight into the way in which patterns break up.
 
This reflects the beginning of the subsequences. There are some emerging methods for analysing over the whole length which may give insight into the way in which patterns break up.
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See also [[HAP table for Sequence of length 1112]]

Latest revision as of 10:02, 12 January 2010

This sequence, of length 1112 (close to the current record) may be of interest because it was derived differently from the 1124 sequences, by a depth-first search starting with a sequence of length 974 satisfying 1=-2=-5 and 11=-13 exactly:

0+--+-++--+--+-++-++--+-++-++--+-++--+--+-++-++--+-++--+--+-
++-++----++-++--+-++--+--+-+++-+--+-+--++--+-++-++--+-++--+-
-+-++--+-++-+++-+--+-++--+--+-++-++--+--+-++--+-++--++-+-+-+
+---+-++-++---+++--+--+-++-++--+--+--+-++-++--+--+-++-++--+-
++--+--+-++-++--++---++--+-+-+++--+-++--++---++-+--++-++--+-
-+-++--+-++-++--+-++--++-+--+-+--+++-+--+-++---++--++--+++-+
--+-+-+--+++-+-++----++-+++--+-+--+-++--+-++-++--+-++--+--++
+---+-+--++++---+--+-+++---++-++--+-++--+--+-++--+-++-++--+-
-+-++++---+-++--++-+-++--+--+-++-+--+++-+--+--+-++-++--++---
-+-++-++-++----++-++---++++-+----++--++++--+-++--+--+-++-++-
+---+--+-++-++--++-+--+--+-++-++-++--+--+-++---+++--+-++-++-
--+++--+---++--++-++--++-+-+--+-+-+--++++--+---+++-++--++---
+++---+--+++--+++--+---+++-++----++-+++-+--+--+--+-+-++++---
++--+-++--+--+-++-++-++--+-++--+--+-+--++--+-++-++--+-++--+-
-+++---++-+-++-+-+--++-+--+-+-++--+--+-++++---+-+--+++---+++
-+--+++---+--+-++++--+--++--++---++-++--+-++--++--+++--+--++
+--++--+---++++--++---++-+-++-+-+---++-+---+++-+--++--+++---
-++++--+--+-+-++-+-+--+++--+-++-+--+--+++---+-++---++-++--+-
+--++--+-+-+-++--++-++--+++-+---+

As expected the subsequence structure is very similar to that for the 974 sequence

617: 1 4 10 13 16 19 22 25 27 31 34 40 42 46 52 55 58 64 76 82 85

3478: 2 5 8 11 17 20 21 23 26 29 32 38 41 44 50 54 59 62 65 68 80 83


809: 18 37 45 72 79

3286; 9 36 74


873: 7 28 49 70

3222: 14 35 47 56 77


1458: 3 12 30 39 48 57 66 75

2637: 6 15 24 33 43 51 60 63 69 78


242: 67 845: 73 1266: 53 1430: 84 1833: 61 3314: 71 3506: 81

This reflects the beginning of the subsequences. There are some emerging methods for analysing over the whole length which may give insight into the way in which patterns break up.

See also HAP table for Sequence of length 1112