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
Amiram Eldar, Table of n, a(n) for n = 1..10000
Chris K. Caldwell, Cunningham Chains.
FORMULA
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)))
(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