Talk:Hofstadter Figure-Figure sequences

No max n

That statement is there to explicitly exclude solutions that used a fixed sized array, say of a 1000 elements and an empty array, then moved elements between the two arrays.

Mind you, an algorithm that started with fixed array sizes and doubled their sizes as necessary would be OK. --Paddy3118 08:37, 22 October 2011 (UTC)

S(n)

The sequence S(n) is further defined as the sequence of positive integers not present in R(n).

I think this should be S(n) is defined as the nth integer in the sequence of positive integers not present in R(n). If S(n) is itself a sequence then R(n) would be a sequence, but the example R(n) values suggest that R is a sequence and R(n) is an integer from that sequence. --Rdm 16:34, 22 October 2011 (UTC)

Hmm. You're right, but then I can't help but think that S(n) can stand for both an integer given a particular value of n, or the sequence when thinking of n as being an arbitrary value? It seems to me that it can be either or both, but either way, would you go further and say that you could not determine the meaning of the sentence?

I'm inclined to leave it as-is. --Paddy3118 17:44, 22 October 2011 (UTC)

In the general case, yes, we might use S(n) to refer to a sequence. However, for this to be accurate, n needs to be an unbound value. And in that particular sentence, we are talking about n having a specific value (which is used in R(n)). Anyways, from my point of view the phrasing is confusing (and opens up questions like: is it possible for S(n) to contain values for some value of n which are not present in later values of n? And rather than delve into the issues that I would need to tackle to determine whether or not this could be a relevant topic, I would rather the notation be self consistent). --Rdm 17:56, 22 October 2011 (UTC)