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%I #31 Sep 08 2022 08:44:47
%S 3,5,23,59,73,79,109,179,269,373,383,389,409,439,509,599,683,709,929,
%T 983,1019,1129,1193,1409,1423,1453,1663,1699,1879,2039,2053,2069,2579,
%U 2753,2963,3049,3169,3203,3259,3719,3769,3833,4799,4973,4993,5303,5443,5483
%N Primes p such that 3*p + 4 and 9*p + 16 are also prime.
%C Original name: Numbers n such that n remains prime through 2 iterations of the function f(x) = 3x + 4.
%C n, 3*n + 4, 9*n + 16 are primes. - _Vincenzo Librandi_, Aug 04 2010
%C Except for a(2) = 5, all terms are congruent to 3 or 9 (mod 10). If p == 1 (mod 10), 3p + 4 == 7 (mod 10) could be prime, but then 9p + 16 == 5 (mod 10). - _Alonso del Arte_, Nov 23 2018
%H Harvey P. Dale, <a href="/A023247/b023247.txt">Table of n, a(n) for n = 1..1000</a>
%e 3 * 3 + 4 = 11, which is prime, and 3 * 11 + 4 = 37, which is also prime, so 3 is in the sequence.
%e 3 * 5 + 4 = 19, which is prime, and 3 * 19 + 4 = 61, which is also prime, so 5 is in the sequence.
%e 3 * 7 + 4 = 25 = 5^2, so 7 is not in the sequence.
%e Although 3 * 11 + 4 = 37, which is prime, 3 * 37 = 115 = 5 * 23, so 11 is not in the sequence.
%t Select[Prime[Range[800]], And@@PrimeQ[Rest[NestList[3# + 4 &, #, 2]]] &] (* _Harvey P. Dale_, Jan 21 2014 *)
%o (Magma) [n: n in [0..100000] | IsPrime(n) and IsPrime(3*n+4) and IsPrime(9*n+16)] // _Vincenzo Librandi_, Aug 04 2010
%o (PARI) select( is(p)=isprime(3*p+4)&&isprime(9*p+16)&&isprime(p), primes([2,5500]) \\ Defines the is() function. The select() command provides a check & illustration. isprime(p) at the end improves performance if a selection is operated on primes as here. - _M. F. Hasler_, Nov 23 2018
%Y Cf. A000040 (primes), A016777 (3n+1, so A016777(n+1) = 3n+4).
%K nonn
%O 1,1
%A _David W. Wilson_
%E Better name from _M. F. Hasler_, Nov 23 2018
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