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

1,1

Comments

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.

Primes p such that 2p + 1 is prime and p != 3 (mod 4); i.e., {A005384} - {A002515}.

2 Union {primes p such that 2p + 1 is prime and p == 1 (mod 4); i.e., 2 Union {A002145 Intersection A005384}.

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.

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 *)

Prog

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

Crossrefs

Cf. A002145, A002515, A005384, A163782.

Sequence in context: A213995 A370513 A134449 * A161500 A061351 A126107

Adjacent sequences: A103576 A103577 A103578 * A103580 A103581 A103582

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 23 2005

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Jul 07 2009

Status

approved