Primes p for which the polynomial (x^47 - 1)/(x - 1) mod p is irreducible.
5, 11, 13, 19, 23, 29, 31, 41, 43, 47, 67, 73, 107, 109, 113, 127, 137, 139, 151, 163, 167, 179, 181, 193, 199, 211, 223, 227, 229, 233, 257, 293, 311, 313, 317, 349, 359, 367, 373, 389, 409, 419, 421, 433, 443, 449, 461, 463, 467, 499, 503, 509, 547, 557
1
This is the 46th-degree cyclotomic polynomial. These primes p satisfy the congruence p mod 47 == {0, 5, 10, 11, 13, 15, 19, 20, 22, 23, 26, 29, 30, 31, 33, 35, 38, 39, 40, 41, 43, 44, 45}. The fraction of all primes in this sequence is 11/23. If we plotted n versus primepi(s(n)), then the plotted points would be very close to the line having slope 23/11.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Wikipedia, Cyclotomic polynomial
(Mma) t = {}; n = 47; p = 1; While[Length[t] < 100, p = NextPrime[p]; If[Length[FactorList[(x^n - 1)/(x - 1), Modulus -> p]] == 2, AppendTo[t, p]]]; t
Cf. A045309, A042993, A045401, S000762-S000782.
nonn
T. D. Noe, Dec 01 2015