Talk:Sylvester's sequence

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	This article is within the scope of WikiProject Mathematics.
	Mathematics grading:	GA Class	Mid Importance	Field: Number theory

Sylvester's sequence (reviewed version) has been listed as a good article under the good-article criteria. If you can improve it further, please do. If it no longer meets these criteria, you can delist it, or ask for a review.

I removed the factorizations of e_1 through e_5, because since most of them are prime, it was pretty pointless. The fact that 1807 = 13 * 139 is very easy to calculate. It is for the larger terms that I think it's actually useful to list prime factors. PrimeFan 19:06, 26 May 2006 (UTC)

1807 being composite is sufficiently nonobvious that in one version of the article I erroneously wrote that the first five terms are prime. So I think it's worth mentioning that one, at least in the text as we do now if not in the actual table. —David Eppstein 00:23, 30 November 2006 (UTC)

[edit] Comment on importance

Mid importance is about right for a general content encyclopedia. Sylvester's sequence has applications in several different problems, most of them relating to Egyptian fractions. If this was, say, PlanetMath or MathWorld, importance would have to be set to high. That is, if PlanetMathers could stop thinking about homeomorphisms and fictional curvature tensors for a couple of minutes. PrimeFan 23:01, 5 December 2006 (UTC)

I'm happy with mid importance also. To me the part about it being the fastest-growing rational series is a better argument for notability than the Egyptian fraction connection (much as I like Egyptian fractions) but neither is enough for me to call it of high importance. And the criterion for low importance says something about "could be trivial" which seems clearly untrue for this subject. So mid is a good fit. Should I ask what a "fictional curvature tensor" is? —David Eppstein 23:06, 5 December 2006 (UTC)

Yes inportance is a tricky one for maths articles. There are only 4 levels, which does not really leave enough scope to fit in 10 thousand maths articles. For me much of the importance characterisation is on how broad the concept is across all mathematical diciplines, possibly also encompassing depth. I find the grading of biographies from Wikipedia:WikiProject Biography/Core biographies more statisfying

Top - Must have had a large impact outside of their main discipline, across several generations, and in the majority of the world.

High - Must have had a large impact in their main discipline (i.e all of mathematics), across a couple of generations. Had some impact outside their country of origin.

Mid - Important in their discipline

Low - A contributor to their discipline and is included in Wikipedia to expand depth of knowledge of other articles.

this does not really cover the different fields of mathematics, so Sylvester's sequence are important in number theroy but not really of impact on other fields like geometry. Really I feel a need for a level between mid and low, for topics important in one field but not of wide importance across the whole of mathematics. --Salix alba (talk) 00:29, 6 December 2006 (UTC)

You don't think the question of which series can converge to a rational is a topic that goes beyond number theory? —David Eppstein 00:39, 6 December 2006 (UTC)

I think the graphical representation shows that Sylvester's sequence could have some application in geometry, but I can't say what that application would be right now. BTW, my compliments to the illustrator! PrimeFan 18:42, 6 December 2006 (UTC)

Thanks, again! BTW, the inspiration for the image was a comment by Nestor Romeral Andres on the OEIS page. —the illustrator (David Eppstein 19:08, 6 December 2006 (UTC))

I found another application to differential geometry this time; see the Boyer et al reference in the article. —David Eppstein 19:06, 8 December 2006 (UTC)

[edit] Good Article review

I've promoted this to a Good Article. Few inline cites, but that's ok for a math article given that everything is referenced, and there's no real ambiguity about what claims are referenced where. Twinxor t 09:23, 6 December 2006 (UTC)

[edit] Question open??

Has it been proven that 0, 1, 2, 3, and 5 are the only values of n for which Sylvester(n) is prime?? This article says it is composite for all n 4-18 except 5. Georgia guy 18:22, 8 December 2006 (UTC)

I don't know of any such proof, although Sylvester himself mentioned the question of primality of these numbers. I imagine that the problem is of similar difficulty to that of primality of the Fermat numbers. —David Eppstein 19:06, 8 December 2006 (UTC)