A330488 - OEIS

%I #22 Dec 19 2019 09:50:57

%S 5,11,107,419,431,461,1019,1289,1301,1427,1481,2087,3119,3467,3539,

%T 4091,4241,5279,5651,5849,5867,6689,7331,8819,9419,9461,9929,10037,

%U 10091,11117,11831,11939,14627,16139,16361,17207,17387,17681,18041,18311,20639,20771,22277,22961,23027,23201,25847

%N Primes p such that p+2 is prime and p+A001414(p+1)+(p+2) is prime.

%C If q, 18*q-1, 18*q+1 and 37*q+8 are prime, then 18*q-1 is in the sequence. Dickson's conjecture implies that there are infinitely many such q, and thus that this sequence is infinite.

%H Robert Israel, <a href="/A330488/b330488.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 107 is in the sequence because 107 and 109 are primes, A001414(108) = 2*2+3*3 = 13, and 107+13+109 = 229 is prime.

%p filter:= proc(p) isprime(p) and isprime(p+2) and isprime(2*p+2+add(s[1]*s[2],s=ifactors(p+1)[2]))  end proc:select(filter, [seq(i,i=5..10^5,6)]);

%o (PARI) \\ using A001414(n) written by _M. F. Hasler_

%o A001414(n)=(n=factor(n))[,1]~*n[,2];

%o forprime(p=3,26000,my(pp1=p+1);if(isprime(p+2),if(isprime(A001414(pp1)+2*pp1),print1(p,", ")))) \\ _Hugo Pfoertner_, Dec 17 2019

%Y Cf. A001414. Subsequence of A001359.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Dec 16 2019