A362914 a(n) = size of largest subset of {1..n} such that no difference between two terms is a prime.

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, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19

Offset

1,2

Comments

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

Links

Martin Ehrenstein, Table of n, a(n) for n = 1..127

Ben Green, On Sarkozy's theorem for shifted primes, Number Theory Web Seminar, May 11 2023; Youtube video https://www.youtube.com/watch?v=5JH_YshJoCo.

Formula

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

Example

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

Crossrefs

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.

Sequence in context: A292027 A025845 A347755 * A029393 A275150 A303904

Adjacent sequences: A362911 A362912 A362913 * A362915 A362916 A362917

Keyword

nonn

Author

N. J. A. Sloane, May 15 2023

Extensions

a(12)-a(40) from Zachary DeStefano, May 15 2023

a(41)-a(75) from Martin Ehrenstein, May 16 2023

Status

approved