OFFSET
1,2
COMMENTS
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.
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
LINKS
Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
Wikipedia, Aurifeuillean factorization
MATHEMATICA
Do[p=Prime[n]; If[PrimeQ[Cyclotomic[2n, n]], Print[p]], {n, 100}]
PROG
(PARI) is(n)=ispseudoprime(polcyclo(2*n, n)) \\ Charles R Greathouse IV, May 22 2017
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
T. D. Noe, Oct 20 2003
STATUS
approved