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%I #19 Sep 24 2024 09:22:02
%S 6,12,138,150,192,348,642,1020,1092,1230,1620,1788,1932,2112,2142,
%T 2238,2658,2688,2730,3330,3540,3918,4002,4158,5010,5640,6090,6450,
%U 6552,6702,7950,8088,9000,9042,9240,9462,9768,10008,10092,10272,10302,10332
%N At these values of k the first, 2nd and 3rd cyclotomic polynomials all give prime numbers.
%C Numbers k such that k-1, k+1 and k^2+k+1 are all primes.
%H Amiram Eldar, <a href="/A070020/b070020.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5000 from Michael De Vlieger)
%e For k = 6: 5, 7 and 43 are prime values of the first 3 cyclotomic polynomials.
%t psQ[n_]:=And@@PrimeQ[{n-1,n+1,n^2+n+1}]; Select[Range[11000],psQ] (* _Harvey P. Dale_, Nov 05 2011 *)
%t Select[Range[10500], AllTrue[Cyclotomic[Range@ 3, #], PrimeQ] &] (* _Michael De Vlieger_, Dec 08 2018 *)
%o (PARI) is(k) = isprime(k-1) && isprime(k+1) && isprime(k^2+k+1); \\ _Amiram Eldar_, Sep 24 2024
%Y Cf. A070155, A070156, A070157, A000068, A006313, A006314, A006315, A006316, A056993, A056994, A056995, A005574, A057465, A057002, A070025, A070042.
%K easy,nonn
%O 1,1
%A _Labos Elemer_, May 07 2002