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A070020
At these values of k the first, 2nd and 3rd cyclotomic polynomials all give prime numbers.
4
6, 12, 138, 150, 192, 348, 642, 1020, 1092, 1230, 1620, 1788, 1932, 2112, 2142, 2238, 2658, 2688, 2730, 3330, 3540, 3918, 4002, 4158, 5010, 5640, 6090, 6450, 6552, 6702, 7950, 8088, 9000, 9042, 9240, 9462, 9768, 10008, 10092, 10272, 10302, 10332
OFFSET
1,1
COMMENTS
Numbers k such that k-1, k+1 and k^2+k+1 are all primes.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Michael De Vlieger)
EXAMPLE
For k = 6: 5, 7 and 43 are prime values of the first 3 cyclotomic polynomials.
MATHEMATICA
psQ[n_]:=And@@PrimeQ[{n-1, n+1, n^2+n+1}]; Select[Range[11000], psQ] (* Harvey P. Dale, Nov 05 2011 *)
Select[Range[10500], AllTrue[Cyclotomic[Range@ 3, #], PrimeQ] &] (* Michael De Vlieger, Dec 08 2018 *)
PROG
(PARI) is(k) = isprime(k-1) && isprime(k+1) && isprime(k^2+k+1); \\ Amiram Eldar, Sep 24 2024
KEYWORD
easy,nonn
AUTHOR
Labos Elemer, May 07 2002
STATUS
approved