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).

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, 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, 51, 55, 0, 53, 0, 59, 57, 53, 59, 55, 0, 65, 0, 59, 65, 69, 0, 71, 69, 65, 71, 71, 0, 53

Offset

1,6

Comments

a(m) = 0 for m in A014092.

Links

Table of n, a(n) for n=1..78.

Example

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.

Mathematica

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

Crossrefs

Cf. A014092, A061358, A338768.

Sequence in context: A318261 A343996 A118362 * A258273 A205680 A137695

Adjacent sequences: A339017 A339018 A339019 * A339021 A339022 A339023

Keyword

nonn

Author

Wesley Ivan Hurt, Nov 22 2020

Status

approved