Primes p for which the polynomial (x^31 - 1)/(x - 1) mod p is irreducible.
3, 11, 13, 17, 31, 43, 53, 73, 79, 83, 127, 137, 167, 179, 197, 199, 229, 239, 241, 251, 269, 313, 331, 353, 383, 389, 487, 499, 509, 569, 571, 601, 613, 631, 641, 673, 757, 761, 787, 797, 809, 823, 827, 859, 881, 911, 941, 947, 983, 1009, 1013, 1097, 1109
1
This is the 30th-degree cyclotomic polynomial. These primes p satisfy the congruence p mod 31 == {0, 3, 11, 12, 13, 17, 21, 22, 24}. The fraction of all primes in this sequence is 4/15. If we plotted n versus primepi(s(n)), then the plotted points would be very close to the line having slope 15/4.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Wikipedia, Cyclotomic polynomial
(Mma) t = {}; n = 31; 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