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%I #59 Apr 18 2023 14:45:51
%S 2,5,29,41,53,89,113,173,233,281,293,509,593,641,653,761,809,953,1013,
%T 1049,1229,1289,1409,1481,1601,1733,1889,1901,1973,2069,2129,2141,
%U 2273,2393,2549,2693,2741,2753,2969,3329,3389,3413,3449,3593,3761,3821,4073,4349,4373,4409,4481,4733,4793,5081
%N Sophie Germain primes that are not Lucasian primes: primes p not 3 (mod 4) such that 2p + 1 is prime.
%C Sophie Germain primes A005384 are those primes p such that 2p + 1 is also prime. Lucasian primes A002515 are those primes p such that p == 3 (mod 4) with 2p + 1 prime.
%C Primes p such that 2p + 1 is prime and p != 3 (mod 4); i.e., {A005384} - {A002515}.
%C 2 Union {primes p such that 2p + 1 is prime and p == 1 (mod 4); i.e., 2 Union {A002145 Intersection A005384}.
%C For n > 1, the prime 2*a(n) + 1 is the smallest prime divisor of (2^a(n) + 1)/3. - _Emmanuel Vantieghem_, Aug 12 2018
%C Primes p such that 2*p+1 divides 2^p+1. - _Hilko Koning_, Sep 21 2021
%C Subset of Josephus_2 primes {A163782} that are themselves also prime. - _Joe Nellis_, Dec 27 2022
%H Harvey P. Dale, <a href="/A103579/b103579.txt">Table of n, a(n) for n = 1..1000</a>
%H Luis Henri Gallardo, <a href="http://www.math.nthu.edu.tw/~amen/2023/AMEN-220120.pdf">Bell Numbers Modulo p</a>, Appl. Math. E-Notes (2023) Vol. 23, 40-48. See p. 43.
%p select(t -> isprime(t) and isprime(2*t+1),[2,seq(4*k+1,k=1..10000)]); # _Robert Israel_, May 20 2015
%t Select[Prime[Range[500]], PrimeQ[2#+ 1 ] && Mod[#, 4] != 3 &] (* _Harvey P. Dale_, Jun 15 2013 *)
%t Select[4Range[100] + 1, PrimeQ[#] && PrimeQ[2# + 1] &] (* _Alonso del Arte_, Jun 01 2019 *)
%o (PARI) forprime(p=2,10^4,if((p%4!=3)&&isprime(2*p+1),print1(p,", "))); \\ _Joerg Arndt_, Nov 18 2014
%Y Cf. A002145, A002515, A005384, A163782.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Mar 23 2005
%E More terms from _Vladimir Joseph Stephan Orlovsky_, Jul 07 2009
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