A156658 Primes p such that also 2*p+1 or (p-1)/2 is prime.

2, 3, 5, 7, 11, 23, 29, 41, 47, 53, 59, 83, 89, 107, 113, 131, 167, 173, 179, 191, 227, 233, 239, 251, 263, 281, 293, 347, 359, 383, 419, 431, 443, 467, 479, 491, 503, 509, 563, 587, 593, 641, 653, 659, 683, 719, 743, 761, 809, 839, 863, 887, 911, 953, 983, 1013

Offset: 1

Author

Reinhard Zumkeller, Feb 13 2009

Keywords

• nonn

Comments

Union of A005384 and A005385;

The intersection of A005384 and A005385 is given by A059455.

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

primes occurring in Cunningham chains of the first kind.

A156876 gives the number of these numbers <= n. [Reinhard Zumkeller, Feb 18 2009]

Links

• Robert Price, Table of n, a(n) for n = 1..14198
• Wikipedia, Sophie Germain prime
• Wikipedia, Safe prime
• Wikipedia, Cunningham chain

Crossrefs

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

Programs

Maple

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

Mathematica

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

PARI

lista(nn) = {forprime(p=2, nn, if (isprime(2*p+1) || isprime((p-1)/2), print1(p, ", ")););} \\ Michel Marcus, Apr 06 2016