cp's OEIS Frontend

A265481 Numbers k such that 9^k - 3^k - 1 is prime.

%I A265481 #31 Sep 08 2022 08:46:14
%S A265481 1,2,3,6,7,20,35,36,140,523,1170,1731,1842,3727,3886,9270,11071,13823,
%T A265481 14451,27086,27606,31876,78008
%N A265481 Numbers k such that 9^k - 3^k - 1 is prime.
%C A265481 For k = 1, 2, 3, 6, 7, 20, 35, the corresponding primes are 5, 71, 701, 530711, 4780781, 12157665455570144399, 2503155504993241551284026887086141.
%C A265481 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).
%C A265481 Conjectures: a(n) is not of the form 7*k+4 or 8*k.
%C A265481 a(17) = 11071 mod 7 is 4, so the first half of the conjecture above is not true. - _Robert Price_, Sep 25 2019
%C A265481 a(23) = 78008 is divisible by 8, so the second half of the conjecture above is not true. - _Robert Price_, Sep 25 2019
%C A265481 a(24) > 2*10^5. - _Robert Price_, Apr 21 2020
%e A265481 6 is in the sequence because 9^6 - 3^6 - 1 = 530711 is prime.
%t A265481 Select[Range[1500], PrimeQ[9^# - 3^# - 1] &]
%o A265481 (Magma) [n: n in [0..500] | IsPrime(9^n-3^n-1)];
%o A265481 (PARI) is(n)=ispseudoprime(9^n - 3^n - 1) \\ _Anders Hellström_, Dec 09 2015
%Y A265481 Cf. numbers n such that k^(2*n)-k^n-1 is prime: A098845 (k=2), this sequence (k=3), A265482 (k=4), A265483 (k=5), A265484 (k=6), A265485 (k=7), A265486 (k=8), A265487 (k=9), A265383 (k=10), A265683 (k=16).
%K A265481 nonn,more
%O A265481 1,2
%A A265481 _Vincenzo Librandi_, Dec 09 2015
%E A265481 a(17)-a(23) from _Robert Price_, Sep 25 2019