A023308 Primes that remain prime through 4 iterations of the function f(x) = 3x + 4.

3203, 21683, 34613, 52813, 103843, 116933, 117443, 165443, 172933, 193603, 195053, 213973, 226783, 321053, 322193, 357613, 360323, 362233, 363403, 368743, 472393, 474143, 496333, 518543, 528673, 569083, 571303, 631853, 654623, 714893, 758503

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

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

All a(n) == 33 or 53 (mod 70). - John Cerkan, Oct 04 2016

Links

• John Cerkan, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A023209, A023247, A023278, and A034936.

Programs

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

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

Maple

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

Mathematica

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

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)
forprime(p=1, 760000, if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Dec 07 2018