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A289109 Primes p that remain prime through 3 iterations of function f(x) = 6x - 1.

%I A289109 #19 May 10 2020 22:26:35
%S A289109 239,269,439,569,599,829,1429,3389,6379,7159,7649,8779,8969,10799,
%T A289109 10939,12919,13729,13879,15649,17159,18149,19379,21649,22669,23929,
%U A289109 24799,25679,26849,28219,30389,30689,33749,34759,36109,36209,36899,40759,47659,49639,52369
%N A289109 Primes p that remain prime through 3 iterations of function f(x) = 6x - 1.
%C A289109 All the terms are congruent to 9 (mod 10). The iteration of f(x) on a term of this sequence then produces primes congruent to 3, 7, 1 (mod 10), followed by a nontrivial multiple of 5.
%H A289109 Robert Israel, <a href="/A289109/b289109.txt">Table of n, a(n) for n = 1..10000</a>
%e A289109 239 is prime and 6 * 239 - 1 = 1433, which is also prime. 6 * 1433 - 1 = 8597, which is also prime. 6 * 8597 = 51581, which is also prime. 6 * 51581 - 1 = 309485 = 5 * 11 * 17 * 331, which is composite, but the previous three primes are enough for 239 to be in the sequence.
%e A289109 241 is not in the sequence because 6 * 241 - 1 = 1445 = 5 * 17^2, which is composite.
%p A289109 filter:= x -> andmap(isprime, [x,6*x-1,36*x-7,216*x-43]):
%p A289109 select(filter, [seq(i,i=9..60000,10)]); # _Robert Israel_, May 10 2020
%t A289109 Select[Prime[Range[15000]], And @@ PrimeQ[NestList[6 # - 1 &, #, 3]] &]
%o A289109 (PARI) forprime(p= 1, 100000, if(isprime(6*p-1) && isprime(36*p-7) && isprime(216*p-43) , print1(p, ", ")));
%Y A289109 Cf. A057326, A057327, A057328, A057329, A057330, A158015.
%K A289109 nonn
%O A289109 1,1
%A A289109 _K. D. Bajpai_, Jun 24 2017