A302564 a(n) is the greatest prime p such that (2*n+1-p)/2 is prime.

3, 5, 7, 7, 11, 13, 13, 17, 19, 19, 23, 23, 17, 29, 31, 31, 29, 37, 37, 41, 43, 43, 47, 47, 41, 53, 53, 47, 59, 61, 61, 59, 67, 67, 71, 73, 73, 71, 79, 79, 83, 83, 53, 89, 89, 83, 89, 97, 97, 101, 103, 103, 107, 109, 109, 113, 113, 107, 113, 103, 113, 107, 127, 127, 131, 131, 113, 137, 139, 139

Offset: 3

Author

Robert Israel, Aug 15 2018

Keywords

• nonn

Comments

Lemoine's conjecture, also called Levy's conjecture, says a(n) exists for all n >= 3.

Links

• Robert Israel, Table of n, a(n) for n = 3..10000
• Wikipedia, Lemoine's conjecture

Crossrefs

Cf. A046927, A103506.

Programs

Maple

Lemoine:= proc(x) local s;
s:= x;
while s > 3 do
  s:= prevprime(s);
  if isprime((x-s)/2) then return s fi
od;
end proc:
seq(Lemoine(2*n+1),n=3..100);

PARI

a(n) = {my(p = precprime(2*n+1)); while (!isprime((2*n+1-p)/2), p = precprime(p-1)); p;} \\ Michel Marcus, Aug 16 2018