I didn't know about Sloane's gap. Very interesting! I was wrong: the first number that is less common in the OEIS than its successor is 14, not 11. I don't know what the situation is if one restricts to increasing sequences; can anyone look into this? Jim Propp On Sunday, January 5, 2014, David Makin wrote:
Not sure about sorting all numbers in terms of interest - but clearly the *most* interesting have to be 0 and 1 ;)
On 5 Jan 2014, at 23:07, W. Edwin Clark wrote:
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<javascript:;>> 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
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