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Primes p such that also 2*p+1 or (p-1)/2 is prime.
3

%I #21 Jul 22 2020 11:39:23

%S 2,3,5,7,11,23,29,41,47,53,59,83,89,107,113,131,167,173,179,191,227,

%T 233,239,251,263,281,293,347,359,383,419,431,443,467,479,491,503,509,

%U 563,587,593,641,653,659,683,719,743,761,809,839,863,887,911,953,983,1013

%N Primes p such that also 2*p+1 or (p-1)/2 is prime.

%C Union of A005384 and A005385;

%C The intersection of A005384 and A005385 is given by A059455.

%C A156660(a(n)) + A156659(a(n)) > 0;

%C primes occurring in Cunningham chains of the first kind.

%C A156876 gives the number of these numbers <= n. [_Reinhard Zumkeller_, Feb 18 2009]

%H Robert Price, <a href="/A156658/b156658.txt">Table of n, a(n) for n = 1..14198</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Sophie_Germain_prime">Sophie Germain prime</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Safe_prime">Safe prime</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Cunningham_chain">Cunningham chain</a>

%p select(t -> isprime(t) and (isprime(2*t+1) or isprime((t-1)/2)), [2,seq(p,p=3..10000,2)]); # _Robert Israel_, May 03 2016

%t Select[Prime@ Range@ 180, PrimeQ[2 # + 1] || PrimeQ[(# - 1)/2] &] (* _Michael De Vlieger_, Apr 06 2016 *)

%o (PARI) lista(nn) = {forprime(p=2, nn, if (isprime(2*p+1) || isprime((p-1)/2), print1(p, ", ")););} \\ _Michel Marcus_, Apr 06 2016

%Y Cf. A005384, A005385, A059500, A156659, A156660, A156876.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Feb 13 2009