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A059453
Sophie Germain primes (A005384) that are not safe primes (A005385).
11
2, 3, 29, 41, 53, 89, 113, 131, 173, 191, 233, 239, 251, 281, 293, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 743, 761, 809, 911, 953, 1013, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1451, 1481, 1499, 1511, 1559, 1583, 1601, 1733, 1811, 1889, 1901
OFFSET
1,1
COMMENTS
Except for 2 and 3 these primes are congruent to 5 or 11 modulo 12.
Introducing terms of Cunningham chains of first kind.
LINKS
Chris K. Caldwell, Cunningham Chains.
FORMULA
A156660(a(n))*(1-A156659(a(n))) = 1. - Reinhard Zumkeller, Feb 18 2009
EXAMPLE
89 is a term because (89-1)/2 = 44 is not prime, but 2*89 + 1 = 179 is prime.
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 *)
Select[Prime[Range[300]], PrimeQ[2#+1]&&!PrimeQ[(#-1)/2]&] (* Harvey P. Dale, Nov 10 2017 *)
PROG
(Python)
from itertools import count, islice
from sympy import isprime, prime
def A059453_gen(): # generator of terms
return filter(lambda p:not isprime(p>>1) and isprime(p<<1|1), (prime(i) for i in count(1)))
A059453_list = list(islice(A059453_gen(), 10)) # Chai Wah Wu, Jul 12 2022
(PARI) is(p) = isprime(p) && isprime(2*p+1) && if(p > 2, !isprime((p-1)/2), 1); \\ Amiram Eldar, Jul 15 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 02 2001
STATUS
approved