a(1)=2, a(n+1)=a(n)+p, where p is the largest prime <a(n) if a(n) is odd or the smallest prime >a(n) if a(n) is even.

A277263

a(1)=2, a(n+1)=a(n)+p, where p is the largest prime <a(n) if a(n) is odd or the smallest prime >a(n) if a(n) is even.