A357369 - OEIS

%I #10 Oct 03 2022 08:45:15

%S 3,5,11,13,11,19,53,17,29,467,59,23,41,29,173,31,197,4877,59,41,151,

%T 67,71,47,751,79,53,661,59,89,61,97,101,103,71,109,73,193,113,199,461,

%U 83,1361,223,137,3331,139,2297,149,101,257,1531,107,163,1621,397,751,997,113,7741,181,313,191,193

%N a(n) is the first prime p such that (p+q)/(2*n) is prime, where q is the next prime after p.

%H Robert Israel, <a href="/A357369/b357369.txt">Table of n, a(n) for n = 2..10000</a>

%e a(4) = 11 because (11+13)/(2*4) = 3 is prime, and no smaller prime works.

%p V:= Vector(100): count:= 0:

%p q:= 3:

%p while count < 99 do

%p   p:= q; q:= nextprime(q);

%p   m:= (p+q)/2;

%p   for r in numtheory:-factorset(m) do

%p     v:= m/r;

%p     if v <= 100 and V[v] = 0 then

%p       count:= count+1; V[v]:= p;

%p     fi

%p   od

%p od:

%p convert(V[2..100],list);

%Y Cf. A357373.

%K nonn

%O 2,1

%A _Robert Israel_, Sep 25 2022