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%I #21 Sep 08 2022 08:46:14
%S 1,3,10,18,70,585,921,1943,4635,13543,13803,15938,39004
%N Numbers k such that 81^k - 9^k - 1 is prime.
%C 2*a(n) is in A265481.
%C For k = 1, 3, 10, 18 the corresponding primes are 71, 530711, 12157665455570144399, 22528399544939174261745512577773519.
%C a(n) is not of the form 5*k+2 (divisibility by 11), 9*k+2 (divisibility by 19), 7*k+2*(-1)^k+7 (divisibility by 29), 15*k+2 (divisibility by 31) or 29*k+8 (divisibility by 59).
%C a(14) > 10^5. - _Robert Price_, Apr 21 2020
%e 3 is in the sequence because 81^3 - 9^3 - 1 = 530711 is prime.
%t Select[Range[1000], PrimeQ[81^# - 9^# - 1] &]
%o (Magma) [n: n in [0..500] | IsPrime(81^n-9^n-1)];
%o (PARI) for(n=1, 1e3, if(ispseudoprime(81^n - 9^n - 1), print1(n, ", "))) \\ _Altug Alkan_, Dec 12 2015
%Y Cf. similar sequences listed in A265481.
%K nonn,more
%O 1,2
%A _Vincenzo Librandi_, Dec 12 2015
%E a(9) from _Altug Alkan_, Dec 12 2015
%E a(10)-a(13) computed from A265481 by _Ray Chandler_, Sep 25 2019
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