A278869 - OEIS

%I #16 Dec 03 2016 12:23:33

%S 11,23,53,173,233,593,653,1103,1223,2693,2903,2963,4793,5303,6263,

%T 6323,7823,9473,10253,11783,12653,13463,15803,20753,25673,27743,27773,

%U 29873,31253,33623,38183,38453,39233,40283,41603,44273,44543,54443,54773,59393,60083,62213

%N Sophie Germain primes p such that p+6 and p-6 are primes.

%C Intersection of A005384 and A006489.

%C After a(1), all the terms are congruent to 3 mod 10.

%C A prime p is Sophie Germain prime if 2*p+1 is also prime.

%H K. D. Bajpai, <a href="/A278869/b278869.txt">Table of n, a(n) for n = 1..9180</a>

%e 11 is in the list because: 2*11 + 1 = 23 (prime), hence 11 is Sophie Germain prime; also, 11 - 6 = 5 and 11 + 6 = 17 are both prime.

%e 23 is in the list because: 2*23 + 1 = 47 (prime), hence 23 is Sophie Germain prime; also, 23 - 6 = 17 and 23 + 6 = 29 are both prime.

%t Select[Prime[Range[20000]], PrimeQ[2 # + 1] && PrimeQ[# + 6] && PrimeQ[# - 6] &]

%o (PARI) forprime(p=1,10000, if(isprime(2*p+1) && isprime(p+6) && isprime(p-6), print1(p, ", ")))

%Y Cf. A000040, A005384, A006489.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Nov 29 2016