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A023308
Primes that remain prime through 4 iterations of the function f(x) = 3x + 4.
2
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
1,1
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
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 *)
PROG
(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
(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
(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
CROSSREFS
Subsequence of A023209, A023247, A023278, and A034936.
Sequence in context: A035777 A108001 A212074 * A171350 A251396 A054036
KEYWORD
nonn
STATUS
approved