A302564 - OEIS

%I #16 Aug 16 2018 13:26:29

%S 3,5,7,7,11,13,13,17,19,19,23,23,17,29,31,31,29,37,37,41,43,43,47,47,

%T 41,53,53,47,59,61,61,59,67,67,71,73,73,71,79,79,83,83,53,89,89,83,89,

%U 97,97,101,103,103,107,109,109,113,113,107,113,103,113,107,127,127,131,131,113,137,139,139

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

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

%H Robert Israel, <a href="/A302564/b302564.txt">Table of n, a(n) for n = 3..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lemoine%27s_conjecture">Lemoine's conjecture</a>

%p Lemoine:= proc(x) local s;

%p s:= x;

%p while s > 3 do

%p   s:= prevprime(s);

%p   if isprime((x-s)/2) then return s fi

%p od;

%p end proc:

%p seq(Lemoine(2*n+1),n=3..100);

%o (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

%Y Cf. A046927, A103506.

%K nonn

%O 3,1

%A _Robert Israel_, Aug 15 2018