A191060 Primes that are not squares mod 11.

2, 7, 13, 17, 19, 29, 41, 43, 61, 73, 79, 83, 101, 107, 109, 127, 131, 139, 149, 151, 167, 173, 193, 197, 211, 227, 233, 239, 241, 263, 271, 277, 281, 283, 293, 307, 337, 347, 349, 359, 373, 409, 431, 439, 457, 461, 479, 491, 503, 523, 541, 547, 557, 563

Offset: 1

Author

T. D. Noe, May 25 2011

Keywords

• nonn
• easy

Comments

Inert rational primes in the field Q(sqrt(-11)). - N. J. A. Sloane, Dec 25 2017

These are also the primes p for which the polynomial x^3 - x^2 - x - 1 (mod p) has only one integer root. This is important for the Fibonacci and Lucas 3-step recursions, A000073 and A001644. See A106276. - T. D. Noe, Apr 17 2012

It appears that these are the primes p such that the sequence p^(5*n) mod 11 has period length 2, repeating [1, 10]. - Gary Detlefs, May 18 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index to sequences related to decomposition of primes in quadratic fields

Programs

Magma

[p: p in PrimesUpTo(563) | JacobiSymbol(p, 11) eq -1]; // Vincenzo Librandi, Sep 11 2012

Mathematica

Select[Prime[Range[200]], JacobiSymbol[#, 11] == -1 &]