A059452 Safe primes (A005385) which are not Sophie Germain primes.

7, 47, 59, 107, 167, 227, 263, 347, 383, 467, 479, 503, 563, 587, 839, 863, 887, 983, 1187, 1283, 1307, 1319, 1367, 1487, 1523, 1619, 1823, 1907, 2027, 2099, 2207, 2447, 2579, 2879, 2999, 3119, 3167, 3203, 3467, 3947, 4007, 4079, 4127, 4139, 4259, 4283

Offset

1,1

Comments

A156659(a(n))*(1-A156660(a(n))) = 1. - Reinhard Zumkeller, Feb 18 2009

Links

Table of n, a(n) for n=1..46.

C. K. Caldwell, Cunningham Chain

W. Roonguthai, Yves Gallot's Proth.exe and Cunningham Chains

Example

347 is here because 173 is a prime but 695 is not. Except for 7, these primes are congruent to 11 modulo 12. Terminal primes in complete Cunningham chains of first kind, i.e., the chains cannot be continued from these primes.

Mathematica

lst={}; Do[p=Prime[n]; If[PrimeQ[(p-1)/2], If[ !PrimeQ[2*p+1], AppendTo[lst, p]]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 24 2009 *)

Prog

(Python)
from itertools import count, islice
from sympy import isprime, prime
def A059452_gen(): # generator of terms
    return filter(lambda p:isprime(p>>1) and not isprime(p<<1|1), (prime(i) for i in count(1)))
A059452_list = list(islice(A059452_gen(), 10)) # Chai Wah Wu, Jul 12 2022

Crossrefs

Cf. A005384, A005385, A053176, A059452-A059456, A007700, A005602, A023272, A023302, A023330.

Sequence in context: A263920 A124837 A122731 * A245229 A141882 A240569

Adjacent sequences: A059449 A059450 A059451 * A059453 A059454 A059455

Keyword

nonn

Author

Labos Elemer, Feb 02 2001

Extensions

Broken link updated by R. J. Mathar, Apr 12 2010

Status

approved