Many excellent designs for a new banner were submitted. We will use the best of them in rotation.
A120392
a(1)=least k such that p(1)=(k*3)^2 + k*3 -1 is prime (so a(1)=1 as 3^2+3-1= 11 = p(1) = prime), then a(n+1)=least k such that (k*p(n))^2 + k*p(n) -1 = p(n+1) = prime.