cp's OEIS Frontend

A338570 Primes p such that q*r mod p is prime, where q is the prime preceding p and r is the prime following p.

%I A338570 #8 Nov 03 2020 11:45:41
%S A338570 11,13,19,29,31,37,47,53,59,67,73,83,89,109,127,131,151,163,173,179,
%T A338570 211,239,251,263,269,283,307,337,359,373,383,421,433,443,449,467,479,
%U A338570 499,503,523,541,547,569,593,599,607,653,659,677,757,787,797,829,853,877,907,919,947,967,971,977,1033
%N A338570 Primes p such that q*r mod p is prime, where q is the prime preceding p and r is the prime following p.
%C A338570 Primes p such that -A049711(p)*A013632(p) mod p is prime.
%C A338570 Includes primes p such that p-8, p-2 and p+4 are also prime.  Dickson's conjecture implies that there are infinitely many of these.
%H A338570 Robert Israel, <a href="/A338570/b338570.txt">Table of n, a(n) for n = 1..10000</a>
%e A338570 a(3) = 19 is a member because 19 is prime, the previous and following primes are 17 and 23, and (17*23) mod 19 = 11 is prime.
%p A338570 R:= NULL: p:= 0: q:= 2: r:= 3:
%p A338570 count:= 0:
%p A338570 while count < 100 do
%p A338570   p:= q; q:= r; r:= nextprime(r);
%p A338570   if isprime(p*r mod q) then count:= count+1; R:= R, q;  fi;
%p A338570 od:
%p A338570 R;
%Y A338570 Cf. A013632, A049711, A338566, A338567.
%K A338570 nonn
%O A338570 1,1
%A A338570 _J. M. Bergot_ and _Robert Israel_, Nov 02 2020