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Primes that are not squares mod 11.
4

%I #23 May 22 2022 09:49:36

%S 2,7,13,17,19,29,41,43,61,73,79,83,101,107,109,127,131,139,149,151,

%T 167,173,193,197,211,227,233,239,241,263,271,277,281,283,293,307,337,

%U 347,349,359,373,409,431,439,457,461,479,491,503,523,541,547,557,563

%N Primes that are not squares mod 11.

%C Inert rational primes in the field Q(sqrt(-11)). - _N. J. A. Sloane_, Dec 25 2017

%C 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

%C 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

%H Vincenzo Librandi, <a href="/A191060/b191060.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="https://oeis.org/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>

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

%o (Magma) [p: p in PrimesUpTo(563) | JacobiSymbol(p, 11) eq -1]; // _Vincenzo Librandi_, Sep 11 2012

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 25 2011