A362915 - OEIS

%I #13 May 18 2023 07:37:24

%S 1,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,6,6,6,6,6,6,6,

%T 6,6,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,

%U 8,8,8,8,8,8,8,8,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,12,12,12,12,12,12,12

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

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

%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.

%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: A362914.

%K nonn

%O 1,2

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

%E a(1)-a(40) from _Zachary DeStefano_, May 15 2023, a(41)-a(100) from _Rob Pratt_, May 15 2023.