1,1

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.

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

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.

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

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, ", ")));

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

Sequence in context: A279274 A282812 A140032 * A247888 A243102 A294092

Adjacent sequences: A289106 A289107 A289108 * A289110 A289111 A289112

K. D. Bajpai, Jun 24 2017

approved