Primes p for which the polynomial (x^41 - 1)/(x - 1) mod p is irreducible.
7, 11, 13, 17, 19, 29, 41, 47, 53, 67, 71, 89, 97, 101, 149, 151, 157, 179, 181, 193, 199, 211, 227, 229, 233, 239, 257, 263, 281, 293, 311, 313, 317, 347, 397, 421, 439, 457, 463, 479, 499, 503, 509, 521, 557, 563, 587, 593, 641, 643, 673, 691, 709, 719
1
This is the 40th-degree cyclotomic polynomial. These primes p satisfy the congruence p mod 41 == {0, 6, 7, 11, 12, 13, 15, 17, 19, 22, 24, 26, 28, 29, 30, 34, 35}. The fraction of all primes in this sequence is 2/5. If we plotted n versus primepi(s(n)), then the plotted points would be very close to the line having slope 5/2.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Wikipedia, Cyclotomic polynomial
(Mma) t = {}; n = 41; 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