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A023242 Primes that remain prime through 2 iterations of function f(x) = 2x + 3.

%I A023242 #32 Sep 08 2022 08:44:47
%S A023242 2,5,7,13,43,47,67,97,113,137,167,173,197,277,307,397,463,467,557,607,
%T A023242 617,887,1063,1153,1217,1237,1307,1373,1427,1453,1523,1553,1567,1663,
%U A023242 1693,2027,2113,2143,2203,2617,2647,2707,2777,2857,2927,3343,3613,3767
%N A023242 Primes that remain prime through 2 iterations of function f(x) = 2x + 3.
%C A023242 Primes p such that 2*p + 3 and 4*p + 9 are also primes. - _Vincenzo Librandi_, Aug 04 2010
%C A023242 All terms > 5 end in 3 or 7. - _Robert Israel_, Jun 22 2015
%H A023242 Vincenzo Librandi, <a href="/A023242/b023242.txt">Table of n, a(n) for n = 1..7000</a>
%p A023242 select(t -> isprime(t) and isprime(2*t+3) and isprime(4*t+9), [2,seq(2*i+1, i=1..10000)]); # _Robert Israel_, Jun 22 2015
%t A023242 Select[Range[4 10^6], PrimeQ[#]&& PrimeQ[2 # + 3]&&PrimeQ[4 # + 9] &] (* _Vincenzo Librandi_, Jun 24 2014 *)
%o A023242 (Magma) [p: p in PrimesUpTo(10000) | IsPrime(2*p+3) and IsPrime(4*p+9)] // _Vincenzo Librandi_, Aug 04 2010 (simplified by _Bruno Berselli_)
%o A023242 (PARI) is(n)=isprime(n) && isprime(2*n+3) && isprime(4*n+9) \\ _Charles R Greathouse IV_, Sep 09 2014
%o A023242 (Sage) # By the definition:
%o A023242 def t(i): return 2*i+3
%o A023242 [p for p in primes(5000) if is_prime(t(p)) and is_prime(t(t(p)))] # _Bruno Berselli_, Sep 09 2014
%K A023242 nonn,easy
%O A023242 1,1
%A A023242 _David W. Wilson_