A277993 - OEIS

%I #11 Dec 16 2017 11:48:46

%S 23,53,89,113,131,251,293,491,683,719,953,1439,1499,1511,1733,2393,

%T 3491,3779,5171,7043,7151,7433,7649,7901,8069,8663,9689,10781,12011,

%U 12653,13049,13229,13451,13553,14669,15569,16001,16253,18899,19709,20411,22469,22751,23099

%N Sophie Germain primes p such that p + 2 and p - 2 are semiprimes.

%C Intersection of A005384 and A063643.

%H K. D. Bajpai, <a href="/A277993/b277993.txt">Table of n, a(n) for n = 1..4000</a>

%e a(1) = 23 is Sophie Germain prime because 2*23 + 1 = 47 is prime. Also, 23 + 2 = 25 =  5*5; 23 - 2 = 21 = 7*3; are both semiprime.

%e a(2) = 53 is Sophie Germain prime because 2*53 + 1 = 107 is prime. Also, 53 + 2 = 55 =  11*5; 23 - 2 = 51 = 17*3; are both semiprime.

%t Select[Select[Prime[Range[10000]], PrimeQ[2 # + 1] &], PrimeOmega[# - 2] == 2 && PrimeOmega[# + 2] == 2 &]

%t Select[Prime[Range[3000]],PrimeQ[2#+1]&&PrimeOmega[#+{2,-2}]=={2,2}&] (* _Harvey P. Dale_, Dec 16 2017 *)

%o (PARI) is(n) = ispseudoprime(n) && ispseudoprime(2*n+1) && bigomega(n+2)==2 && bigomega(n-2)==2 \\ _Felix Fröhlich_, Nov 07 2016

%Y Cf. A005384, A063637, A063638, A063643.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Nov 07 2016