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

1,1

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A196012 A065104 A138645 * A166246 A250185 A063206

Adjacent sequences: A191057 A191058 A191059 * A191061 A191062 A191063

Keyword

nonn,easy

Author

T. D. Noe, May 25 2011

Status

approved