T m(x) = (+/-)T n(x)
From Polymath Wiki
This sequence, of length 688, satisfies the following relations exactly:
[math]\displaystyle{ x_{2n} = -x_n }[/math]
[math]\displaystyle{ x_{5n} = -x_n }[/math]
[math]\displaystyle{ x_{13n} = -x_{11n} }[/math]
0+--+-++--+--+-++-++--+-++-++- -+-++--+--+-++-++--+-++--+--+- ++-++--+-++-+---+-++--+--+-+++ -+--+-++--+--+-++-++--+-++-++- -+-++----++-++--+--+-++--++-++ +--++--+--+-++--+-++--++-+-+-+ +---+-++--++-+-++-+---+-++-++- -+-++--+-++-+---++-+-++--+--+- +--++--+-++-+++-+--+--+--+-+++ +---+-++--+--+-++-++---+++-+-- -++-+--+-++++---+-++--+--+-++- ++-++----++-++---+++--+--+++-- -++-+++--++--+-++-+----+++--++ -+-++---+-+-++-++--+-++--+--++ +--++--+-++-+---+--+-+++--+-+- ++-+--++--++---++-++--+-++--+- -++++--+--+-++-++--+-++--+---+ ++--+-++--+++---+-++-++--+-+-- -++-+-++--+--+-++-++--+-++-++- -+-++--+--+-+++----+-++--++++- +--+--++--+-++--++-+-+---++++- +---++-+--+++---+-++-++--+--++ ---++--+-++-+-+++----+++-+-++
This also satisfies [math]\displaystyle{ x_{7n} = -x_{11n} }[/math] which is interesting because it was not an original constraint.
The subsequences seem to group as follows (initial numbers are binary coded versions of the first part of each subsequence, the paired sequences are negatives of each other):
617: 1 4 10 16 19 25 31 34 40 46
3478: 2 5 8 17 20 23 32 38 41 47 50
873: 7 13 22 28 33 37 42 49 52
3222: 11 14 21 26 29 35 39 44
1458: 3 12 30 48
2637: 6 15 24 43 51
1833: 18 27 45
2262: 9 36
