Mathematics – Number Theory
Scientific paper
2010-09-21
Mathematics
Number Theory
7 pages
Scientific paper
Let g be the element that is the sum of x^(n^2) for n >= 0 of A=Z/2[[x]], and let B consist of all n for which the coefficient of x^n in 1/g is 1. (The elements of B are the entries 0, 1, 2, 3, 5, 7, 8, 9, 13, ... in A108345; see The On-Line Encyclopedia of Integer Sequences (OEIS).) Cooper, Eichhorn, and O'Bryant [1] have shown that the (upper) density of B is at most 1/4, and it is conjectured that B has density 0. This note uses results of Gauss on sums of 3 squares to show that the subset of B consisting of all n not congruent to 15 mod 16 has density 0. The final section gives some computer calculations, made by Kevin O'Bryant, indicating that, pace [1], B has density 1/32.
Monsky Paul
No associations
LandOfFree
Disquisitiones Arithmeticae and online sequence A108345 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Disquisitiones Arithmeticae and online sequence A108345, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Disquisitiones Arithmeticae and online sequence A108345 will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-697099