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A059453 Sophie Germain primes (A005384) that are not safe primes (A005385).

%I A059453 #27 Jul 15 2024 10:23:48
%S A059453 2,3,29,41,53,89,113,131,173,191,233,239,251,281,293,419,431,443,491,
%T A059453 509,593,641,653,659,683,743,761,809,911,953,1013,1031,1049,1103,1223,
%U A059453 1229,1289,1409,1451,1481,1499,1511,1559,1583,1601,1733,1811,1889,1901
%N A059453 Sophie Germain primes (A005384) that are not safe primes (A005385).
%C A059453 Except for 2 and 3 these primes are congruent to 5 or 11 modulo 12.
%C A059453 Introducing terms of Cunningham chains of first kind.
%H A059453 Amiram Eldar, <a href="/A059453/b059453.txt">Table of n, a(n) for n = 1..10000</a>
%H A059453 Chris K. Caldwell, <a href="https://t5k.org/glossary/page.php/CunninghamChain">Cunningham Chains</a>.
%F A059453 A156660(a(n))*(1-A156659(a(n))) = 1. - _Reinhard Zumkeller_, Feb 18 2009
%e A059453 89 is a term because (89-1)/2 = 44 is not prime, but 2*89 + 1 = 179 is prime.
%t A059453 lst={};Do[p=Prime[n];If[ !PrimeQ[(p-1)/2],If[PrimeQ[2*p+1],AppendTo[lst,p]]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jun 24 2009 *)
%t A059453 Select[Prime[Range[300]],PrimeQ[2#+1]&&!PrimeQ[(#-1)/2]&] (* _Harvey P. Dale_, Nov 10 2017 *)
%o A059453 (Python)
%o A059453 from itertools import count, islice
%o A059453 from sympy import isprime, prime
%o A059453 def A059453_gen(): # generator of terms
%o A059453     return filter(lambda p:not isprime(p>>1) and isprime(p<<1|1),(prime(i) for i in count(1)))
%o A059453 A059453_list = list(islice(A059453_gen(),10)) # _Chai Wah Wu_, Jul 12 2022
%o A059453 (PARI) is(p) = isprime(p) && isprime(2*p+1) && if(p > 2, !isprime((p-1)/2), 1); \\ _Amiram Eldar_, Jul 15 2024
%Y A059453 Intersection of A005384 and A059456.
%Y A059453 Cf. A005385, A053176, A059452, A059453, A059454, A059455, A007700, A005602, A023272, A023302, A023330.
%K A059453 nonn
%O A059453 1,1
%A A059453 _Labos Elemer_, Feb 02 2001