A162862 Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime.

1, 5, 17, 20, 21, 30, 53, 60, 86, 137, 172, 195, 212, 224, 229, 258, 268, 272, 319, 339, 355, 365, 366, 389, 390, 398, 414, 467, 480, 504, 534, 539, 543, 567, 592, 619, 626, 654, 709, 735, 756, 766, 770, 778, 787, 806, 812, 874, 943, 973, 1003, 1036, 1040

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 14 2009

Keywords

• nonn

Comments

The associated primes are in A162861.

Numbers n such that Phi(11,n) is prime, where Phi(11,n) = (n^11 - 1)/(n - 1) is the eleventh cyclotomic polynomial. - Jianing Song, Sep 05 2018

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Index to values of cyclotomic polynomials of integer argument

Crossrefs

Cf. A060885, A162861.

Programs

Mathematica

Select[Range[100], PrimeQ[1 + Sum[#^i, {i, 10}]] &] (* Alonso del Arte, Apr 11 2014 *)

PARI

is(n)=isprime(polcyclo(11,n)) \\ Charles R Greathouse IV, Sep 14 2015

Formula

A000040 INTERSECT A060885.