A023242 - OEIS

%I #32 Sep 08 2022 08:44:47

%S 2,5,7,13,43,47,67,97,113,137,167,173,197,277,307,397,463,467,557,607,

%T 617,887,1063,1153,1217,1237,1307,1373,1427,1453,1523,1553,1567,1663,

%U 1693,2027,2113,2143,2203,2617,2647,2707,2777,2857,2927,3343,3613,3767

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

%C Primes p such that 2*p + 3 and 4*p + 9 are also primes. - _Vincenzo Librandi_, Aug 04 2010

%C All terms > 5 end in 3 or 7. - _Robert Israel_, Jun 22 2015

%H Vincenzo Librandi, <a href="/A023242/b023242.txt">Table of n, a(n) for n = 1..7000</a>

%p 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 Select[Range[4 10^6], PrimeQ[#]&& PrimeQ[2 # + 3]&&PrimeQ[4 # + 9] &] (* _Vincenzo Librandi_, Jun 24 2014 *)

%o (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 (PARI) is(n)=isprime(n) && isprime(2*n+3) && isprime(4*n+9) \\ _Charles R Greathouse IV_, Sep 09 2014

%o (Sage) # By the definition:

%o def t(i): return 2*i+3

%o [p for p in primes(5000) if is_prime(t(p)) and is_prime(t(t(p)))] # _Bruno Berselli_, Sep 09 2014

%K nonn,easy

%O 1,1

%A _David W. Wilson_