Longest constrained sequences

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The numbers in square brackets show (what we know of) the longest sequence satisfying the given constraints exactly. The notation [math]a=b[/math] is shorthand for [math]T_a(x) = T_b(x)[/math], and [math]a=-b[/math] for [math]T_a(x) = -T_b(x)[/math].

1 = +2 : [170]
1 = -2 : [>=974]
1 = -2,  1 = -3 : [470]
1 = -2,  1 = +5 : [356]
1 = -2,  1 = -5 : [>=974]
1 = -2,  1 = -5,  11 = -13 [>=974] 
2 = -3 : [>=587]