A place to start with such investigations is perhaps the famous paper on "Sloane's gap" ( http://arxiv.org/pdf/1101.4470.pdf ) which discusses the distribution of N(n) = the number of occurrences of n in the OEIS. On Sun, Jan 5, 2014 at 5:46 PM, James Propp <jamespropp@gmail.com> wrote:
What is the smallest value of n such that n+1 appears in more of the increasing sequences in the OEIS than n does?
The reason I want to restrict attention to increasing sequences in the OEIS is that these correspond to interesting subsets of the positive integers. I suppose if anyone wants to answer my question with the word "increasing" omitted, I'd be interested in that too. Conjecture: The n that you get is the same for both versions of my question. Refined conjecture: in both cases, n is 11.
Jim Propp
On Sunday, January 5, 2014, Charles Greathouse wrote:
I had a similar thought to Kerry's: for some given collection of properties (like those in this site), weight them by how often they show up in the first 10^15 terms (the site's limit) and add up the weights. Which number(s) have the lowest score?
A possible family of weighting functions: f_k(n) = n^-k, where n is the number of occurrences in those terms. So f_0(k) counts properties without regard to how often the occur, f_1(n) counts a property that happens 4 times as often 1/4th the weight, f_{1/2}(n) counts it with 1/2 the weight, etc.
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Sun, Jan 5, 2014 at 3:31 PM, Kerry Mitchell <lkmitch@gmail.com <javascript:;>> wrote:
Certainly, all natural numbers are interesting, but (it seems to me) they are not all equally interesting (or popular or useful or talked-about). So, there's no least-interesting number, but are there less-interesting numbers? Without trying to establish a hierarchy, are there numbers that, by having minimal membership in other groups, are less interesting?
Kerry
On Sun, Jan 5, 2014 at 1:21 PM, Eugene Salamin <gene_salamin@yahoo.com <javascript:;>
wrote:
All natural numbers are interesting because, if there were an uninteresting number, there would be a smallest one, and that number would be interesting by virtue of being the smallest uninteresting number.
-- Gene
________________________________ From: W. Edwin Clark <wclark@mail.usf.edu <javascript:;>> To: math-fun <math-fun@mailman.xmission.com <javascript:;>> Sent: Sunday, January 5, 2014 11:20 AM Subject: [math-fun] Numbers Aplenty
Giovanni Resta's new website Numbers Aplenty<http://www.numbersaplenty.com/>is an impressive implementation of the old idea that every natural number is interesting. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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