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 A339020 #32 Mar 24 2024 09:06:10
%S A339020 0,0,0,0,1,3,3,7,5,5,0,11,9,7,11,7,0,11,15,11,17,19,0,23,21,17,0,19,0,
%T A339020 29,27,23,29,25,0,35,0,27,35,39,0,41,39,39,41,37,0,47,45,41,0,43,0,47,
%U A339020 51,55,0,53,0,59,57,53,59,55,0,65,0,59,65,69,0,71,69,65,71,71,0,53
%N A339020 Largest value of (p*q mod n), for primes p and q, where p + q = n and p <= q (or 0 if no such primes exist).
%C A339020 a(m) = 0 for m in A014092.
%e A339020 a(14) = 7; There are two partitions of 14 into two primes, (3,11) and (7,7). Since (3*11 mod 14) = 5 and (7*7 mod 14) = 7, then 7 is the largest. Therefore, a(14) = 7.
%t A339020 Table[If[n == 1, 0, Max[Table[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]) Mod[i (n - i), n], {i, Floor[n/2]}]]], {n, 100}]
%t A339020 Table[Max[Mod[Times@@#,n]&/@Select[IntegerPartitions[n,{2}],AllTrue[#,PrimeQ]&]],{n,80}]/.(-\[Infinity]->0) (* _Harvey P. Dale_, Mar 24 2024 *)
%Y A339020 Cf. A014092, A061358, A338768.
%K A339020 nonn
%O A339020 1,6
%A A339020 _Wesley Ivan Hurt_, Nov 22 2020