S000762


Primes p for which the polynomial (x^11 - 1)/(x - 1) mod p is irreducible.

2, 7, 11, 13, 17, 19, 29, 41, 61, 73, 79, 83, 101, 107, 127, 139, 149, 151, 167, 173, 193, 211, 227, 233, 239, 271, 277, 281, 283, 293, 337, 347, 349, 359, 409, 431, 457, 479, 491, 503, 523, 541, 547, 557, 563, 569, 601, 607, 613, 673, 677, 701, 733, 739

1

S000762

This is the tenth-degree cyclotomic polynomial. These primes p satisfy the congruence p mod 11 == {0, 2, 6, 7, 8}. 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 = 11; 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. A045309A042993, A045401, S000763-S000782.

nonn

T. D. Noe, Dec 01 2015

© Tony D Noe 2014-2015