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Primes that remain prime through 4 iterations of the function f(x) = 3x + 4.
2

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

%S 3203,21683,34613,52813,103843,116933,117443,165443,172933,193603,

%T 195053,213973,226783,321053,322193,357613,360323,362233,363403,

%U 368743,472393,474143,496333,518543,528673,569083,571303,631853,654623,714893,758503

%N Primes that remain prime through 4 iterations of the function f(x) = 3x + 4.

%C Primes p such that 3*p+4, 9*p+16, 27*p+52 and 81*p+160 are also primes. - _Vincenzo Librandi_, Aug 04 2010

%C All a(n) == 33 or 53 (mod 70). - _John Cerkan_, Oct 04 2016

%H John Cerkan, <a href="/A023308/b023308.txt">Table of n, a(n) for n = 1..10000</a>

%p select(n->isprime(n) and isprime(3*n+4) and isprime(9*n+16) and isprime(27*n+52) and isprime(81*n+160),[$1..760000]); # _Muniru A Asiru_, Dec 07 2018

%t Select[Prime[Range[10000]], Union[PrimeQ[NestList[(3# + 4 &), #, 4]]] == {True} &] (* _Alonso del Arte_, Nov 30 2018 *)

%o (Magma) [n: n in [1..1000000] | IsPrime(n) and IsPrime(3*n+4) and IsPrime(9*n+16) and IsPrime(27*n+52) and IsPrime(81*n+160)] // _Vincenzo Librandi_, Aug 04 2010

%o (PARI) is(n) = my(x=3*n+4, i=0); while(1, if(!ispseudoprime(x), return(0), i++); if(i==4, return(1)); x=3*x+4)

%o forprime(p=1, 760000, if(is(p), print1(p, ", "))) \\ _Felix Fröhlich_, Dec 07 2018

%o (GAP) Filtered([1..760000],n->IsPrime(n) and IsPrime(3*n+4) and IsPrime(9*n+16) and IsPrime(27*n+52) and IsPrime(81*n+160)); # _Muniru A Asiru_, Dec 07 2018

%Y Subsequence of A023209, A023247, A023278, and A034936.

%K nonn

%O 1,1

%A _David W. Wilson_