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%I #16 Sep 26 2019 09:08:24
%S 1,2,3,4,5,9,17,36,157,245,352,3977
%N Numbers k such that Cyclotomic(2k,k) is prime.
%C This is a generalization of A056826. Note that (n^n+1)/(n+1) = cyclotomic(2n,n) when n is prime. These are probable primes for n > 352. No others < 4700.
%C All terms of this sequence that are greater than 3 are congruent to 0 or 1 mod 4. In general, if k = s^2*t where t is squarefree and t == 2, 3 (mod 4), then Cyclotomic(2k,t*x^2) is the product of two polynomials. See the Wikipedia link below. - _Jianing Song_, Sep 25 2019
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CyclotomicPolynomial.html">Cyclotomic Polynomial</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Aurifeuillean_factorization">Aurifeuillean factorization</a>
%t Do[p=Prime[n]; If[PrimeQ[Cyclotomic[2n, n]], Print[p]], {n, 100}]
%o (PARI) is(n)=ispseudoprime(polcyclo(2*n,n)) \\ _Charles R Greathouse IV_, May 22 2017
%Y Cf. A056826 ((k^k+1)/(k+1) is prime), A070519 (cyclotomic(k,k) is prime), A088875 (cyclotomic(k,-k) is prime).
%K hard,nonn
%O 1,2
%A _T. D. Noe_, Oct 20 2003
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