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

239, 269, 439, 569, 599, 829, 1429, 3389, 6379, 7159, 7649, 8779, 8969, 10799, 10939, 12919, 13729, 13879, 15649, 17159, 18149, 19379, 21649, 22669, 23929, 24799, 25679, 26849, 28219, 30389, 30689, 33749, 34759, 36109, 36209, 36899, 40759, 47659, 49639, 52369

Offset: 1

Author

K. D. Bajpai, Jun 24 2017

Keywords

• nonn

Comments

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.

Examples

			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.
241 is not in the sequence because 6 * 241 - 1 = 1445 = 5 * 17^2, which is composite.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A057326, A057327, A057328, A057329, A057330, A158015.

Programs

Maple

filter:= x -> andmap(isprime, [x,6*x-1,36*x-7,216*x-43]):
select(filter, [seq(i,i=9..60000,10)]); # Robert Israel, May 10 2020

Mathematica

Select[Prime[Range[15000]], And @@ PrimeQ[NestList[6 # - 1 &, #, 3]] &]

PARI

forprime(p= 1, 100000, if(isprime(6*p-1) && isprime(36*p-7) && isprime(216*p-43) , print1(p, ", ")));