OFFSET
1,2
COMMENTS
For k = 1, 2, 3, 6, 7, 20, 35, the corresponding primes are 5, 71, 701, 530711, 4780781, 12157665455570144399, 2503155504993241551284026887086141.
a(n) is not of the form 4*k+5 (divisibility by 5) or 5*k+4 (divisibility by 11) or 9*k+4*(-1)^k (divisibility by 19).
Conjectures: a(n) is not of the form 7*k+4 or 8*k.
a(17) = 11071 mod 7 is 4, so the first half of the conjecture above is not true. - Robert Price, Sep 25 2019
a(23) = 78008 is divisible by 8, so the second half of the conjecture above is not true. - Robert Price, Sep 25 2019
a(24) > 2*10^5. - Robert Price, Apr 21 2020
EXAMPLE
6 is in the sequence because 9^6 - 3^6 - 1 = 530711 is prime.
MATHEMATICA
Select[Range[1500], PrimeQ[9^# - 3^# - 1] &]
PROG
(Magma) [n: n in [0..500] | IsPrime(9^n-3^n-1)];
(PARI) is(n)=ispseudoprime(9^n - 3^n - 1) \\ Anders Hellström, Dec 09 2015
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Vincenzo Librandi, Dec 09 2015
EXTENSIONS
a(17)-a(23) from Robert Price, Sep 25 2019
STATUS
approved