Real-rooted atlas

Root regions

Nodes grouped by the interval that contains every root of every row (proved, for all n). A node can have several proved regions; the sharpest is the smallest interval.

All roots inNodes
(-inf, 0] 2294
(-inf, +inf) 332
(-inf, 0) 258
(-inf, -1] 188
[-1, 0] 147
[−3−2√2, −3+2√2] (rational outer bound [-1564556493/268435456, -46056243/268435456]) 13
[-1, 0) 13
(-inf, 1] 10
[0, +inf) 6
(-4, 0) 6
(-1, 0) 6
(-2, 0) 6
(-5, -1) 6
(-1, 0] 3
[-4, 0] 3
(0, 1) 3
(-3, 1] 3
(-1, 3] 3
(3, 7] 3
(-4, 0] 3
(-1, 1) 3
(-2, 2) 2
(11, 15] 2
(2, 6] 2
(1, 5] 2
(4, 8] 2
(0, 4] 2
(-2, 2] 2
(5, 9] 2
(-2, -1) 2
[9/2, +inf) 2
(41/3, 15] 1
(8, 12] 1
(-1, 3) 1
[-5, -1] 1
(-3, 2) 1
(-8, 0) 1
(0, 4) 1
(2, 10] 1
(6, 8] 1
[2, +inf) 1
(-5, 3] 1
(-inf, 1/2] 1
(3, 7) 1
(5, 7] 1
(86/9, 10] 1
(-1, 7] 1
(-9, -1) 1
(0, 8] 1
(7, 11] 1
[-3/2, +inf) 1
(-2, 3) 1
[5, +inf) 1
(-6, 0) 1
(-inf, 3/2] 1
(13, 15] 1
(32/3, 12] 1
(5/3, 3] 1
[-1, -2/3) 1
(-1/3, 1] 1
[11/2, +inf) 1
(-4, 4] 1
(-inf, -2] 1
(20/3, 8] 1
(4, 12] 1
(7, 9] 1
(-3, -1) 1
[7/2, +inf) 1
(-7, -1) 1
(14/3, 6] 1
(50/9, 6] 1
(-2, -1] 1
[15/2, +inf) 1
(-4/9, 0] 1
(10, 12] 1
(23/9, 3] 1
(8, 10] 1
(-1, 1] 1
[-4/9, 0] 1
(-7, 1] 1
(0, 2] 1
(17/3, 7] 1
(6, 10] 1
[-1/2, +inf) 1
(-2, 0] 1
[19/2, +inf) 1
(-5, -1] 1
(104/9, 12] 1
(3, 5] 1
(41/9, 5] 1
(8/3, 4] 1
[-8, 0] 1
(-3, 5] 1
(-8, 0] 1
(2, 4] 1
(68/9, 8] 1
[-2, 0] 1
[3/2, +inf) 1
(-6, -2) 1
(-inf, 1/4] 1
(11/3, 5] 1
[-1, -1/2) 1
(-1/2, 0] 1
[1, +inf) 1
(1, 3] 1
(2/3, 2] 1
(7, 15] 1
[-36, 0) 1
(-2, 6] 1
[5/2, +inf) 1
(-6, 2] 1
(-inf, 5/2] 1
(131/9, 15] 1
(32/9, 4] 1
(5/9, 1] 1
[-1, +inf) 1
[13/2, +inf) 1
(-4/3, 0] 1
(1, 9] 1
(23/3, 9] 1
(4, 6] 1
(77/9, 9] 1
[-4/3, 0] 1
(-3, 1) 1
(-7, -3) 1
(0, 1] 1
(14/9, 2] 1
(59/9, 7] 1
[17/2, +inf) 1
(10, 14] 1
(26/3, 10] 1

Nodes with all roots in (-3, -1) (1)