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A236171 Numbers k such that k^2 - k - 1, k^3 - k - 1, and k^4 - k - 1 are all prime.

%I A236171 #13 Mar 21 2020 07:13:32
%S A236171 4,9,11,16,55,60,71,189,361,450,469,669,1261,1351,1490,1591,2101,2254,
%T A236171 2396,2594,3774,3866,4011,5375,5551,5840,6070,7336,7545,7666,7735,
%U A236171 8105,8255,9825,10525,11621,12100,13084,13454
%N A236171 Numbers k such that k^2 - k - 1, k^3 - k - 1, and k^4 - k - 1 are all prime.
%H A236171 Amiram Eldar, <a href="/A236171/b236171.txt">Table of n, a(n) for n = 1..10000</a>
%e A236171 3866^2 - 3866 - 1, 3866^3 - 3866 - 1, and 3866^4 - 3866 - 1 are all prime, so 3866 is a member of this sequence.
%t A236171 Select[Range[15000], And @@ PrimeQ[#^Range[2, 4] - # - 1] &] (* _Amiram Eldar_, Mar 21 2020 *)
%o A236171 (Python)
%o A236171 import sympy
%o A236171 from sympy import isprime
%o A236171 {print(n) for n in range(10**5) if isprime(n**2-n-1) and isprime(n**3-n-1) and isprime(n**4-n-1)}
%o A236171 (PARI)
%o A236171 s=[]; for(n=1, 20000, if(isprime(n^2-n-1) && isprime(n^3-n-1) && isprime(n^4-n-1), s=concat(s, n))); s \\ _Colin Barker_, Jan 20 2014
%Y A236171 Cf. A002328, A126421, A126424.
%K A236171 nonn
%O A236171 1,1
%A A236171 _Derek Orr_, Jan 19 2014