A103579 Sophie Germain primes that are not Lucasian primes: primes p not 3 (mod 4) such that 2p + 1 is prime.

2, 5, 29, 41, 53, 89, 113, 173, 233, 281, 293, 509, 593, 641, 653, 761, 809, 953, 1013, 1049, 1229, 1289, 1409, 1481, 1601, 1733, 1889, 1901, 1973, 2069, 2129, 2141, 2273, 2393, 2549, 2693, 2741, 2753, 2969, 3329, 3389, 3413, 3449, 3593, 3761, 3821, 4073, 4349, 4373, 4409, 4481, 4733, 4793, 5081

Offset: 1

Author

Jonathan Vos Post, Mar 23 2005

Keywords

• easy
• nonn

Comments

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

Primes p such that 2*p+1 divides 2^p+1. - Hilko Koning, Sep 21 2021

Subset of Josephus_2 primes {A163782} that are themselves also prime. - Joe Nellis, Dec 27 2022

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Luis Henri Gallardo, Bell Numbers Modulo p, Appl. Math. E-Notes (2023) Vol. 23, 40-48. See p. 43.

Crossrefs

Cf. A002144, A002515, A005384, A163782.

Programs

Maple

select(t -> isprime(t) and isprime(2*t+1),[2,seq(4*k+1,k=1..10000)]); # Robert Israel, May 20 2015

Mathematica

Select[Prime[Range[500]], PrimeQ[2#+ 1 ] && Mod[#, 4] != 3 &] (* Harvey P. Dale, Jun 15 2013 *)
Select[4Range[100] + 1, PrimeQ[#] && PrimeQ[2# + 1] &] (* Alonso del Arte, Jun 01 2019 *)

PARI

forprime(p=2,10^4,if((p%4!=3)&&isprime(2*p+1),print1(p,", "))); \\ Joerg Arndt, Nov 18 2014

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Jul 07 2009