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Primes that remain prime through 5 iterations of function f(x) = 3x + 10.
1

%I #24 Sep 08 2022 08:44:47

%S 233,709,11699,16417,24481,31663,63317,94999,172279,185243,205081,

%T 228713,240347,266681,285539,334511,372059,395719,479327,583501,

%U 734197,786613,856627,863711,1146091,1187167,1188259,1423067,1534591,1562269,1594301

%N Primes that remain prime through 5 iterations of function f(x) = 3x + 10.

%C Primes p such that 3*p+10, 9*p+40, 27*p+130, 81*p+400 and 243*p+1210 are also primes. - _Vincenzo Librandi_, Aug 05 2010

%H John Cerkan, <a href="/A023338/b023338.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) == 9 (mod 14). - _John Cerkan_, Oct 11 2016

%t rp5Q[p_]:=AllTrue[Rest[NestList[3#+10&,p,5]],PrimeQ]; Select[Prime[ Range[ 150000]],rp5Q] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 17 2020 *)

%o (Magma) [n: n in [1..25000000] | IsPrime(n) and IsPrime(3*n+10) and IsPrime(9*n+40) and IsPrime(27*n+130) and IsPrime(81*n+400) and IsPrime(243*n+1210)] // _Vincenzo Librandi_, Aug 05 2010

%o (PARI) is(n)=isprime(n) && isprime(3*n+10) && isprime(9*n+40) && isprime(27*n+130) && isprime(81*n+400) && isprime(243*n+1210) \\ _Charles R Greathouse IV_, Oct 11 2016

%Y Subsequence of A023211, A023249, A023280, and A023310.

%K nonn

%O 1,1

%A _David W. Wilson_

%E Definition clarified by _Harvey P. Dale_, Mar 17 2020