

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, 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
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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}]


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



