A362914 - OEIS

%I #34 May 18 2023 07:40:02

%S 1,2,2,2,2,2,2,2,3,3,4,4,4,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,9,

%T 9,9,10,10,10,10,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,14,15,

%U 15,15,15,16,16,16,16,17,17,17,17,18,18,18,18,19,19,19

%N a(n) = size of largest subset of {1..n} such that no difference between two terms is a prime.

%C Suggested by Ben Green's Number Theory Web Seminar on May 11 2023.

%H Martin Ehrenstein, <a href="/A362914/b362914.txt">Table of n, a(n) for n = 1..127</a>

%H Ben Green, On Sarkozy's theorem for shifted primes, <a href="https://www.ntwebseminar.org/previous-talks">Number Theory Web Seminar</a>, May 11 2023; Youtube video https://www.youtube.com/watch?v=5JH_YshJoCo.

%F Taking numbers of the form 4k + 1 <= n gives a(n) >= 1 + floor((n - 1) / 4). - _Zachary DeStefano_, May 16 2023

%e The first few examples where a(n) increases are {1}, {1,2}, {1,5,9}, and {1,2,10,11}.

%Y Other entries of the form "size of largest subset of {1...n} such that no difference between two terms is ...": a square: A100719; a prime - 1: A131849; a prime + 1: A362915.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, May 15 2023

%E a(12)-a(40) from _Zachary DeStefano_, May 15 2023

%E a(41)-a(75) from _Martin Ehrenstein_, May 16 2023