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%I #20 Apr 03 2023 10:36:09
%S 2,3,29,41,53,89,113,131,173,191,233,239,251,281,293,419,431,443,491,
%T 509,593,641,653,659,683,743,761,809,911,953,1013,1031,1049,1103,1223,
%U 1229,1289,1409,1451,1481,1499,1511,1559,1583,1601,1733,1811,1889,1901
%N Sophie Germain primes (A005384) which are not safe primes (A005385).
%C A156660(a(n))*(1-A156659(a(n))) = 1. - _Reinhard Zumkeller_, Feb 18 2009
%H C. K. Caldwell, <a href="https://t5k.org/glossary/page.php/CunninghamChain">Cunningham Chains</a>
%e 89 is here because (89-1)/2=44 is not prime, but 2*89 + 1 = 179 is prime. Except for 2 and 3 these primes are congruent to 5 or 11 modulo 12. Introducing terms of Cunningham chains of first kind.
%t 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 Select[Prime[Range[300]],PrimeQ[2#+1]&&!PrimeQ[(#-1)/2]&] (* _Harvey P. Dale_, Nov 10 2017 *)
%o (Python)
%o from itertools import count, islice
%o from sympy import isprime, prime
%o def A059453_gen(): # generator of terms
%o return filter(lambda p:not isprime(p>>1) and isprime(p<<1|1),(prime(i) for i in count(1)))
%o A059453_list = list(islice(A059453_gen(),10)) # _Chai Wah Wu_, Jul 12 2022
%Y Cf. A005384, A005385, A053176, A059452-A059456, A007700, A005602, A023272, A023302, A023330.
%K nonn
%O 1,1
%A _Labos Elemer_, Feb 02 2001
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