

A289109


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


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
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OFFSET

1,1


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.


LINKS

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


EXAMPLE

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.


MAPLE

filter:= x > andmap(isprime, [x, 6*x1, 36*x7, 216*x43]):
select(filter, [seq(i, i=9..60000, 10)]); # Robert Israel, May 10 2020


MATHEMATICA

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


PROG

(PARI) forprime(p= 1, 100000, if(isprime(6*p1) && isprime(36*p7) && isprime(216*p43) , print1(p, ", ")));


CROSSREFS

Cf. A057326, A057327, A057328, A057329, A057330, A158015.
Sequence in context: A279274 A282812 A140032 * A247888 A243102 A294092
Adjacent sequences: A289106 A289107 A289108 * A289110 A289111 A289112


KEYWORD

nonn


AUTHOR

K. D. Bajpai, Jun 24 2017


STATUS

approved



