A230227 - OEIS

%I #11 Jun 28 2015 10:18:41

%S 5,7,11,13,17,19,23,31,37,41,47,53,59,61,67,79,83,89,97,101,107,109,

%T 131,137,151,157,163,167,173,191,193,199,223,229,251,257,269,277,283,

%U 307,313,317,331,347,353,367,373,397,401,409

%N Primes p with 3*p - 10 also prime.

%C Conjecture: For any integer n > 4 not equal to 76, we have 2*n = p + q for some terms p and q from the sequence.

%C This is stronger than Goldbach's conjecture for even numbers.

%H Zhi-Wei Sun, <a href="/A230227/b230227.txt">Table of n, a(n) for n = 1..10000</a>

%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1211.1588">Conjectures involving primes and quadratic forms</a>, preprint, arXiv:1211.1588.

%e a(1) = 5 since 3*5 - 10 = 5 is prime.

%t PQ[p_]:=PQ[p]=p>3&&PrimeQ[3p-10]

%t m=0

%t Do[If[PQ[Prime[n]],m=m+1;Print[m," ",Prime[n]]],{n,1,80}]

%t Select[Prime[Range[100]],PrimeQ[3#-10]&] (* _Harvey P. Dale_, Jun 28 2015 *)

%Y Cf. A000040, A002375, A230138, A230140, A230141, A230217, A230219, A230223, A230224, A230230.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Oct 12 2013