Second last line was copy-pasted lol. Definitely not necessary.

No.

[ [p, sum of all i_j of I for which p is a prime factor (p positive) of i_j] ...]

[[p, sum of all numbers from the list that are divisible with p]]

p = prime number

It says:

[ [p, sum of all i_j of I for which p is a prime factor (p positive) of i_j] ...]

However, should it not be:

[ [p, sum of all i_j of I for which p is a prime factor (p positive) of the sum] ...]

Depends on how frequently it's used, and to what degree performance matters.

I understood that it was referring to a new concept, but yeah, I also misunderstood the task.

it's not fibonacci, it's TRIbonacci. The description is fine, you just didn't grasp what the task is yet.

"But what if we started with [0, 0, 1] as a signature? As starting with [0, 1] instead of [1, 1] basically shifts the common Fibonacci sequence by once place, you may be tempted to think that we would get the same sequence shifted by 2 places, but that is not the case and we would get: ..."

This is a bit wrong here. The fibonacci sequence becoms a sequence of 0's when "shifted" by 2 places, since by definition, the sequence adds the previous two numbers, not previous three.

Shifting sequence by 2 places gives us:

1: 0
2: 0
3: (1) + (2) = 0 + 0 = 0
4: 0
5: ...

I feel like an edit of the description is necessary.