A339020 - OEIS

%I #32 Mar 24 2024 09:06:10

%S 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 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 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 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 a(m) = 0 for m in A014092.

%e 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 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 Table[Max[Mod[Times@@#,n]&/@Select[IntegerPartitions[n,{2}],AllTrue[#,PrimeQ]&]],{n,80}]/.(-\[Infinity]->0) (* _Harvey P. Dale_, Mar 24 2024 *)

%Y Cf. A014092, A061358, A338768.

%K nonn

%O 1,6

%A _Wesley Ivan Hurt_, Nov 22 2020