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User:Charles R Greathouse IV/Chase sequences

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Chase example.png

What is A179833?

It is defined as "First differences of A179832." A179832 is defined as "Position of ones in A179831", which in turn is defined as "Quadrisection of the fourth central column of triangle A122242, a(n) = A179830((4*n)+1)."

If you follow these sequences and all their descendants, you get something like the graph to the right.

Surely the author of these sequences understood their meanings, and a sufficiently diligent person could no doubt write a program to generate the terms of the original sequence, with subroutines for all the sequences referenced. But a casual observer might be forgiven for failing to understand the significance of the first difference of the position of the ones in the quadrisection of one of the columns of a triangle defined in terms of two other sequences.

I call these chase sequences, because of the process of following one reference after another.

To authors

Chase example 2.png

When you are writing a sequence, please keep your audience in mind. You know your sequences inside and out, but those reading your sequences may not. In any case A-numbers rarely mean anything at a glance, and following links (or looking at title-text) is difficult or impossible in some circumstances (e.g., when the sequence is printed, or when the sequence name is itself in title text). Consider the example: even though the graph is not too complicated, few would understand it from the A-numbers alone.

This doesn't mean you shouldn't refer to other sequences! But it does mean that you should think twice before submitting a sequence with a name which relies on a reference to another sequence, especially if that sequence does the same.

Most sequences that reference another in their name should do so in a way that if the sequence name was obscured, it would still make sense. So

A002182 Highly composite numbers, definition (1): where d(n), the number of divisors of n (Axxxxxx), increases to a record.

is easy to understand even though the A-number has been censored. In those times when it is necessary to define a sequence purely in terms of another (perhaps because the preceding definition is too complex to include), the number of layers of recursion should be strictly limited. Two, or three at most, is the recommended maximum. References can go deeper, but if a reader cannot understand a sequence, or its prerequisite, or the prerequisite to the prerequisite without looking deeper, you should find a way to break the cycle by making at least one of them self-contained. (Of course alternate definitions can be given in the name or comments.)

To readers

If you come across a sequence of this sort, and you can't figure it out, consider contacting its author. If you do manage to understand it, please submit clarification to the sequence, so that future readers will be better able to understand. With any luck this will encourage more contributions to the sequence—perhaps even some answering questions you wondered about!


Of course the particular example used is merely illustrative, and should not be taken as criticism of its author (a valued contributor whose thoughts on keywords, categories, and guided browsing are practically definitive).

See also

External links