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[a1s]

1,1
1,2
1,3
1,4
1,5
1,6
1,7
1,8
1,9
1,10

10,1
10,2
10,3
10,4
10,5
10,6
10,7
10,8
10,9
10,10

[delphonso]

1,2
1,3
1,4
1,5
1,6
1,7
1,9
1,10

10,1
10,8

These do.

[a1s]

Is the pattern:
Each number that isn't 8 or 1 must be followed by 8 or 1, and 8 or 1 must be followed by a number that isn't 8 or 1.

[delphonso]

Is the pattern:
Each number that isn't 8 or 1 must be followed by 8 or 1, and 8 or 1 must be followed by a number that isn't 8 or 1.

That might be true according to the pattern, but it is not the pattern, no.

[a1s]

Is the pattern:
Each number that isn't 8 or 1 must be followed by 8 or 1, and 8 or 1 must be followed by a number that isn't 8 or 1.

That might be true according to the pattern, but it is not the pattern, no.

You have to provide a counterexample (something that fits your pattern but not mine or vice versa)

[delphonso]

Is the pattern:
Each number that isn't 8 or 1 must be followed by 8 or 1, and 8 or 1 must be followed by a number that isn't 8 or 1.

That might be true according to the pattern, but it is not the pattern, no.

You have to provide a counterexample (something that fits your pattern but not mine or vice versa)

Sorry! I'll give a couple.

3, 1, 15, 11, 10
and
9, 8, 7, 1

both fit the pattern.

[coalboat]

8, 2
8, 3
8, 4
8, 5
8, 6
8, 7
8, 9
8, 10
?

[delphonso]

Yes to all.

[coalboat]

1, 2, 8, 3, 10
?

[delphonso]

1, 2, 8, 3, 10
?

No.

[coalboat]

1, 2, 9, 10
?

[delphonso]

No.

[IcyTea31]

[] (empty list)
[1,[]] (list containing the number 1 and an empty list)
[[],8] (list containing an empty list and the number 8 )
[1]
[2]
[8]
[1..] (list containing all positive integers)
[1 : [1..]] (list containing the number 1 followed by all positive integers including 1, i.e. 1,1,2,3,4...)
[1,[1..]] (list containing the number 1, and as a separate element, a list containing all positive integers)
[1,1,1]
[1..1] (list containing an infinite number of 1's)
[-1]
[-2]
[1,-1]
[1,a]

[delphonso]

If I understand that correctly, generally no.

However,
1,2
1,3
and so on were confirmed here.

Spoiler (click to show/hide)

1,2
1,3
1,4
1,5
1,6
1,7
1,9
1,10

10,1
10,8

These do.

Should I give a hint?

[IcyTea31]

Hold up, there must be something about the ordering, since [3,1,2,8,10] passes but [1,2,3,8,10] doesn't. The numbers 1 and 8 are obviously special, as has been proven via the unnecessarily numerous pairings of them with other numbers.

[3,1,2,10,8]
[10,8,2,1,3]
[10,8,3,2,1]
[3,1,2,8,10,1]
[3,1,2,8,10,8]
[3,1,2,8,10,18]
[3,8,2,1,10]