cp's OEIS Frontend

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

%I A303214 #24 Jul 04 2018 20:23:24
%S A303214 3,211,223,479,521,631,673,809,1009,1213,1249,1319,1471,1511,1523,
%T A303214 1543,1693,1721,1801,1823,1901,2081,2111,2203,2309,2411,2459,2591,
%U A303214 2633,2789,2939,3061,3079,3181,3203,3271,3343,3359,3511,3571,3671,3943,4001,4091,4111
%N A303214 Prime numbers whose average with the previous prime is not divisible by 2 or 3.
%C A303214 Very similar to A031931.
%C A303214 3 and all prime(k+1) such that A001223(k) is divisible by 12. - _Robert Israel_, Jul 04 2018
%H A303214 Robert Israel, <a href="/A303214/b303214.txt">Table of n, a(n) for n = 1..10000</a>
%F A303214 2 NOT(|) (p+previous_prime(p))/2 AND 3 NOT(|) (p+previous_prime(p))/2
%e A303214 p = 223 => (p + previous_prime(p))/2 = (223 +211)/2 = 7*31;
%e A303214 p =  53 => (p + previous_prime(p))/2 =  (53 + 51)/2 = 52 (divisible by 2).
%p A303214 count:= 1: Res:= 3:
%p A303214 p:= 3:
%p A303214 while count < 100 do
%p A303214   q:= p; p:= nextprime(p);
%p A303214   v:= (q+p)/2;
%p A303214   if igcd(v,6)=1 then
%p A303214     count:= count+1;
%p A303214     Res:= Res, p;
%p A303214   fi
%p A303214 od:
%p A303214 Res;# _Robert Israel_, Jul 04 2018
%o A303214 (PARI) ok(n)={my(t=n+precprime(n-1)); n > 2 && isprime(n) && t%4 && t%3} \\ _Andrew Howroyd_, Jul 02 2018
%Y A303214 Cf. A001223, A031931.
%K A303214 nonn
%O A303214 1,1
%A A303214 _Olivier Bélot_, Apr 19 2018