This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A224961 #7 Feb 28 2023 15:10:35
%S A224961 0,0,1,2,1,2,2,3,3,2,1,4,0,4,4,4,5,4,4,3,2,4,4,3,5,3,4,4,6,4,7,4,4,7,
%T A224961 5,5,6,5,6,8,5,7,7,6,3,9,5,8,5,8,7,10,9,7,8,8,5,8,8,9,8,8,10,7,11,13,
%U A224961 8,10,10,10,11,9,12,9,13,11,9,12,7,11
%N A224961 a(n) = number of primes of the form p * q + 2 where p is the prime(n) and q is any prime < p.
%e A224961 For n=4, p=7, there are a(4)=2 solutions from 7*3+2=23 and 7*5+2=37.
%t A224961 Table[p = Prime[n]; c = 0; i = 1; While[i < n, If[PrimeQ[p*Prime[i] + 2], c = c + 1]; i++]; c, {n, 80}]
%t A224961 Table[Count[Prime[n]Prime[Range[n-1]]+2,_?PrimeQ],{n,80}] (* _Harvey P. Dale_, Feb 28 2023 *)
%Y A224961 Cf. A103960, A224748, A210481.
%K A224961 nonn
%O A224961 1,4
%A A224961 _Jayanta Basu_, Apr 21 2013