A303214 Prime numbers whose average with the previous prime is not divisible by 2 or 3.

3, 211, 223, 479, 521, 631, 673, 809, 1009, 1213, 1249, 1319, 1471, 1511, 1523, 1543, 1693, 1721, 1801, 1823, 1901, 2081, 2111, 2203, 2309, 2411, 2459, 2591, 2633, 2789, 2939, 3061, 3079, 3181, 3203, 3271, 3343, 3359, 3511, 3571, 3671, 3943, 4001, 4091, 4111

Offset: 1

Author

Olivier Bélot, Apr 19 2018

Keywords

• nonn

Comments

Very similar to A031931.

3 and all prime(k+1) such that A001223(k) is divisible by 12. - Robert Israel, Jul 04 2018

Examples

			p = 223 => (p + previous_prime(p))/2 = (223 +211)/2 = 7*31;
p =  53 => (p + previous_prime(p))/2 =  (53 + 51)/2 = 52 (divisible by 2).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001223, A031931.

Programs

Maple

count:= 1: Res:= 3:
p:= 3:
while count < 100 do
  q:= p; p:= nextprime(p);
  v:= (q+p)/2;
  if igcd(v,6)=1 then
    count:= count+1;
    Res:= Res, p;
  fi
od:
Res;# Robert Israel, Jul 04 2018

PARI

ok(n)={my(t=n+precprime(n-1)); n > 2 && isprime(n) && t%4 && t%3} \\ Andrew Howroyd, Jul 02 2018

Formula

2 NOT(|) (p+previous_prime(p))/2 AND 3 NOT(|) (p+previous_prime(p))/2